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Single‐model initial‐condition large ensembles are powerful tools to quantify the forced response, internal climate variability, and their evolution under global warming. Here, we present the CMIP6 version of the Max Planck Institute Grand Ensemble (MPI‐GE CMIP6) with currently 30 realizations for the historical period and five emission scenarios. The power of MPI‐GE CMIP6 goes beyond its predecessor ensemble MPI‐GE by providing high‐frequency output, the full range of emission scenarios including the highly policy‐relevant low emission scenarios SSP1‐1.9 and SSP1‐2.6, and the opportunity to compare the ensemble to complementary high‐resolution simulations. First, we describe MPI‐GE CMIP6, evaluate it with observations and reanalyzes and compare it to MPI‐GE. Then, we demonstrate with six application examples how to use the power of the ensemble to better quantify and understand present and future climate extremes, to inform about uncertainty in approaching Paris Agreement global warming limits, and to combine large ensembles and artificial intelligence. For instance, MPI‐GE CMIP6 allows us to show that the recently observed Siberian and Pacific North American heatwaves would only avoid reaching 1–2 years return periods in 2071–2100 with low emission scenarios, that recently observed European precipitation extremes are captured only by complementary high‐resolution simulations, and that 3‐hourly output projects a decreasing activity of storms in mid‐latitude oceans. Further, the ensemble is ideal for estimates of probabilities of crossing global warming limits and the irreducible uncertainty introduced by internal variability, and is sufficiently large to be used for infilling surface temperature observations with artificial intelligence. Plain Language Summary: Climate model simulations that start from different initial states and differ only due to the chaos in the climate system are used extensively to quantify the forced climate response, variability intrinsic to the climate system, and their change under global warming. Here, we present a new version of the Max Planck Institute Grand Ensemble (MPI‐GE CMIP6) that is run as part of the latest generation of climate models. This single‐model ensemble currently consists of 30 realizations for the historical period 1850–2014 and for five scenarios of possible future climates until 2100. The power of MPI‐GE CMIP6 goes beyond its predecessor by not only providing monthly mean but also 3‐hourly to daily model output, the full range of future scenarios including the two highly policy‐relevant scenarios that were designed to match the Paris Agreement global warming limits of 1.5 and 2°C, and the opportunity to compare the low‐resolution ensemble to simulations of the same model version with higher horizontal resolution. In this paper, we describe the new ensemble and demonstrate with application examples how to use its power. Key Points: The Max Planck Institute Grand Ensemble in its CMIP6 version (MPI‐GE CMIP6) is a 30‐member initial‐condition large ensemble with up to 3‐hourly model output and five emission scenariosThe ensemble is specifically suited to investigate climate extremes and Paris Agreement global warming limitsMPI‐GE CMIP6 adequately represents heat extremes, while precipitation extremes are captured by complementary high‐resolution simulations [ABSTRACT FROM AUTHOR]

A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal conditions. Motivated by the subtle dynamics of cell activity in a crustacean central pattern generator (CPG), this paper proposes a refinement of the notion of chaos that reconciles homeostasis and chaos in systems with multiple timescales. We show that systems displaying relaxation cycles while going through chaotic attractors generate chaotic dynamics that are regular at macroscopic timescales and are, thus, consistent with physiological function. We further show that this relative regularity may break down through global bifurcations of chaotic attractors such as crises, beyond which the system may also generate erratic activity at slow timescales. We analyze these phenomena in detail in the chaotic Rulkov map, a classical neuron model known to exhibit a variety of chaotic spike patterns. This leads us to propose that the passage of slow relaxation cycles through a chaotic attractor crisis is a robust, general mechanism for the transition between such dynamics. We validate this numerically in three other models: a simple model of the crustacean CPG neural network, a discrete cubic map, and a continuous flow. [ABSTRACT FROM AUTHOR]

Pelvic floor disorders (PFDs), including fecal and urinary incontinence as well as pelvic organ prolapse, are common medical issues faced by one-third of all women across the lifespan. Despite this prevalence, many women are unaware of them, have highly stigmatized perceptions of them, and thus do not actively seek support or treatment for them. Given that PFDs can drastically impact quality of life to the point of social isolation and depression, this study examines chaos and desire as both lived and storied constructs that ultimately influence whether and how women with PFDs assert control over their social and corporeal disruption. Guided by narrative sensibilities and informed by semi-structured interviews with 22 women living with varying PFDs, our analysis highlights how chaos serves as a catalyst for continued chaos (i.e. barriers to seeking medical care), mitigation (i.e. resignation and/or public bodily containment), and/or change (i.e. motivations to seek medical care). These findings offer both theoretical and practical implications for helping individuals grappling with the dis-ease of PFDs (i.e. patients, providers, and practitioners) to envision and act otherwise. [ABSTRACT FROM AUTHOR]

The marketplace of ideas is the Supreme Court’s dominant tool for rationalizing expansive First Amendment safeguards. The model, however, is fundamentally flawed. Enlightenment-based assumptions about truth and human rationality that justices installed into the theory’s foundations have been criticized by scholars and, in the era of powerful algorithms and generative AI, are becoming even more suspect. The space is in a state of chaos. Perhaps chaos theory can help. The theory provides a lens through which to revise marketplace theory and therefore re-examine First Amendment free-expression rationales. Chaos theory identifies that Enlightenment-era positivistic, reductionist thinking fails to account for variables and does not allow for linear outcomes. A chaosinfused marketplace accounts for human diversity and revises truth assumptions. [ABSTRACT FROM AUTHOR]

To effectively manage a crisis, most decisions made by governments, organizations, communities, and individuals are based on "shared situational awareness" (SSA) derived from multiple information sources. Developing SSA depends on the alignment of mental models, which "represent our shared version of truth and reality on which we can act." Social media has facilitated public sensemaking during a crisis; however, it has also encouraged mental model dissonance, resulting in the digital destruction of mental models and undermining adequate SSA. The study is concerned with the challenges of creating SSA during the COVID‐19 pandemic in Australia. This paper documents a netnography of Australian public health agencies' Facebook communication, exploring the initial impact of COVID‐19 on SSA creation. Chaos theory is used as a theoretical lens to examine information perception, meaning, and assumptions relating to SSA from pre to post‐pandemic periods. Our study highlights how the initial COVID‐19 "butterfly effect" swamped the public health communication channel, leaving little space for other important health issues. This research contributes to information systems, information science, and communications by illustrating how the emergence of a crisis impacts social media communication, the creation of SSA, and what this means for social media adoption for crisis communication purposes. [ABSTRACT FROM AUTHOR]

The Paleoproterozoic was an important stage in the evolution of life and the environment during Earth's history. Understanding astronomical rhythms and solar system behavior in the Paleoproterozoic is often challenging. In this study, ∼190 m high‐resolution magnetic susceptibility (MS) and ∼30 m high‐resolution Ba/Al data are used to conduct cyclostratigraphic analyses of the Chuanlinggou Formation in the Yanliao Rift, North China Craton. Spectral analysis indicates significant peaks at wavelengths of 12.1–7.7, 2.8–1.6, 0.58–0.33, and 0.29–0.22 m, which matches well with the astronomical cycles predicted by Waltham for ∼1,640 Ma. A 9.9‐Myr astronomical time scale is constructed by tuning the MS series to the 405‐kyr‐long eccentricity cycle. The geological records show ∼1.56‐Myr very long eccentricity period and ∼1.0‐Myr very long obliquity period (close to 3(s4 − s3) − 2(g4 − g3) = 0) in the Paleoproterozoic. The sea‐level change curve predicted by dynamic noise models reveals a significant ∼1.0‐Myr period, indicating that sea level fluctuation may have been driven by the very long obliquity period. Bayesian inversion is used to further estimate the evolution of the ancient Earth‐Moon orbital parameters, constraining a precession rate of 87.14 ± 0.25 arcsec/year and an Earth‐Moon distance of 341,530 ± 390 km for the Paleoproterozoic Changcheng System. These results indicate that astronomical orbital forcing may have played an important role in climate and sea‐level changes in the Precambrian, increasing the understanding of the fundamentals of global sea level fluctuations, orbitally driven mechanisms and the chaotic behavior of the Precambrian solar system. Plain Language Summary: Orbital parameters and long‐term behavior have changed during geological history. For the first time, we found new resonance states between Mars and Earth (i.e., a very long eccentricity period of ∼1.56 Myr and a very long obliquity period of ∼1.0 Myr) from the geological records of the Paleoproterozoic Changcheng System in the Yanliao Rift of the North China Craton. The reconstructed sea‐level change curve shows a significant ∼1.0‐Myr period, indicating that sea level fluctuations may have been driven by the very long obliquity period in the Precambrian. The orbital parameters in the Paleoproterozoic are recovered using Ba/Al ratios, and the calculated precession constant is 87.14 ± 0.25 arcsec/year. The Earth‐Moon distance was 341,530 ± 390 km, and the length of day (LOD) was 18.06 ± 0.05 hr, which indicates that lunar recession may have been slower in deep time. These results increase the understanding of astronomical rhythms and the chaotic behavior of the solar system in the Precambrian. Key Points: A new Earth‐Mars resonance state (3(s4 − s3) − 2(g4 − g3) = 0) is revealed from the Precambrian geological recordsThe ∼1.0‐Myr very long obliquity period significantly affected sea level fluctuations under the Mesoproterozoic greenhouse climate [ABSTRACT FROM AUTHOR]

Preventing unauthorized access to sensitive data has always been one of the main concerns in the field of information security. Accordingly, various solutions have been proposed to meet this requirement, among which encryption can be considered as one of the first and most effective solutions. The continuous increase in the computational power of computers and the rapid development of artificial intelligence techniques have made many previous encryption solutions not secure enough to protect data. Therefore, there is always a need to provide new and more efficient strategies for encrypting information. In this article, a two-way approach for information encryption based on chaos theory is presented. To this end, a new chaos model is first proposed. This model, in addition to having a larger key space and high sensitivity to slight key changes, can demonstrate a higher level of chaotic behavior compared to previous models. In the proposed method, first, the input is converted to a vector of bytes and first diffusion is applied on it. Then, the permutation order of chaotic sequence is used for diffusing bytes of data. In the next step, the chaotic sequence is used for applying second diffusion on confused data. Finally, to further reduce the data correlation, an iterative reversible rule-based model is used to apply final diffusion on data. The performance of the proposed method in encrypting image, text, and audio data was evaluated. The analysis of the test results showed that the proposed encryption strategy can demonstrate a pattern close to a random state by reducing data correlation at least 28.57% compared to previous works. Also, the data encrypted by proposed method, show at least 14.15% and 1.79% increment in terms of MSE and BER, respectively. In addition, key sensitivity of 10−28 and average entropy of 7.9993 in the proposed model, indicate its high resistance to brute-force, statistical, plaintext and differential attacks. [ABSTRACT FROM AUTHOR]

In this study, the dynamic effects of new product supply chain cooperation behavior on optimal government subsidies and supply chain decision-making are studied by establishing a nonlinear discrete inventory decision system; In this system, the government subsidizes authorized remanufacturers to promote remanufacturing, and cooperative behavior exists in the supply chain of new products. The research method is modeling and simulation of a supply chain system based on nonlinear system dynamics theory. The complexity analysis includes the stability analysis of the decision system, the path of the system into chaos, the change of entropy of the system and the performance in chaos system. Our findings indicate that the optimal government subsidy in the cooperative model is lower than that in the non-cooperative model. Consumer surplus is the main reason for the subsidy difference between the two models. In comparison with the cooperative supply chain, the stability of the non-cooperative supply chain is more easily affected by government subsidies. Further, the market is more likely to enter chaos due to improper adjustment of the new products' inventory with cooperative behavior in the supply chain of new products. When the system enters chaos, the new product supply chain's profit in the cooperative system is more likely to be far lower than the equilibrium profit. This study provides a theoretical reference for supply chain inventory management and government subsidy remanufacturer decision-making from the perspective of dynamic systems science. [ABSTRACT FROM AUTHOR]

Image segmentation is one of the pivotal steps in image processing due to its enormous application potential in medical image analysis, data mining, and pattern recognition. In fact, image segmentation is the process of splitting an image into multiple parts in order to provide detailed information on different aspects of the image. Traditional image segmentation techniques suffer from local minima and premature convergence issues when exploring complex search spaces. Additionally, these techniques also take considerable runtime to find the optimal pixels as the threshold levels are increased. Therefore, in order to overcome the computational overhead and convergence problems of the multilevel thresholding process, a robust optimizer, namely the Levy flight and Chaos theory-based Gravitational Search Algorithm (LCGSA), is employed to perform the segmentation of the COVID-19 chest CT scan images. In LCGSA, exploration is carried out by Levy flight, while chaotic maps guarantee the exploitation of the search space. Meanwhile, Kapur's entropy method is utilized for segmenting the image into various regions based on the pixel intensity values. To investigate the segmentation performance of ten chaotic versions of LCGSA, firstly, several benchmark images from the USC-SIPI database are considered for the numerical analysis. Secondly, the applicability of LCGSA for solving real-world image processing problems is examined by using various COVID-19 chest CT scan imaging datasets from the Kaggle database. Further, an ablation study is carried out on different chest CT scan images by considering ground truth images. Moreover, various qualitative and quantitative metrics are used for the performance evaluation. The overall analysis of the experimental results indicated the efficient performance of LCGSA over other peer algorithms in terms of taking less computational time and providing optimal values for image quality metrics. [ABSTRACT FROM AUTHOR]

Pseudo‐random number generators (PRNGs) are the cornerstone of various fields including computer science, cryptography, and scientific simulation. To generate high‐quality and unpredictable pseudo‐random sequences, many works draw attention to the use of chaos theory and dynamical systems. However, most of them focus on continuous or low‐dimensional chaotic systems with strong temporal correlations or insufficient nonlinear dynamics. Thus, in this study, a new PRNG based on a four‐dimensional discrete system is proposed to solve the aforementioned flaws. The PRNG has been implemented on Xilinx Artix‐7 xc7a100tfgg484‐2, which can generate pseudo‐random sequences at a high speed of 12811.53 Mb/s without additional post‐processing. All these sequences have successfully passed the NIST SP800.22 standard test. Both throughput and randomness quality of the proposed PRNG outperform the state‐of‐the‐art. [ABSTRACT FROM AUTHOR]

There are various indicators, i.e., Relative Strength Index (RSI) [1] [2], Moving Average Convergence Divergence (MACD) [3] [4] [5] [6], Stochastic Oscillator [7] [8] applications, to determine market movements with buying and selling decisions in computational Finance, but they have drawbacks that induced discrepancies to match against the best trading times at fixed order-triggering boundaries and delay problems. For example, RSI [1] [2]'s 70 and 30 overbuy and oversell are fixed boundaries. Orders can only be triggered when RSI's value exceeds one of these boundaries, its computation only considers past market condition prompting indicators like RSI to trigger orders with delay. In this paper, we proposed a method to reduce these problems with advanced AI technologies to generate indicators' buy and sell signals in the best trading time. Recurrent Neural Network (RNN) [9] has outstanding performance to learn time-series data automatic with long-time sequences but its ordinary RNN units [10] [11] such as Long-Short-Term-Memory(LSTM)[12] are unable to decipher the relationships between time units called context. Hence, researchers have proposed an algorithm based on RNNs' Attention Mechanism [13] [14] allowing RNNs to learn information such as chaotic attributes [15] [16] [17] [18] and Quantum properties [19] [20] [21] contained in time sequences. Chaos Theory [15] [16] and Quantum Finance Theory (QFT) [22] are also proposed to simulate these two features (or attributes?). Quantum Price Level (QPL) [22] [23] is one of the well-formed QFT models to simulate all possible vibration levels to locate price. The system used in this paper consists of two components 1) neural network to predict future data and solve indicators lagging problem, and 2) fuzzy logic to solve fixed order-triggering boundaries problem. Its system design has two main parts 1) Chaotic HLCO Predictor consists of LSTM, Lee-Oscillator and attention mechanism to predict the High, Low, Close and Open, 2) QPL-based Fuzzy Logic Trading Strategy to receive the result and trigger trading signals. This new proposed model has obtained significant results in backtesting previous data and outperformed other traditional indicators to facilitate investment decisions when market changes constantly. Codes are available at https://github.com/JarvisLee0423/ Chaotic Quantum Finance AI Predicted Trading System. [ABSTRACT FROM AUTHOR]

This paper presents an overview of the history and recent efforts in combining chaos theory and evolutionary computation techniques. Various algorithms from the evolutionary computation domain, also known as metaheuristic algorithms, have been successfully enhanced with chaotic components in the past. Numerous ways to incorporate chaos have been examined, and many impressive results have been reported. Implementations of discrete chaotic maps such as Lozi, Hénon, and logistic map as generators of chaotic pseudo-random sequences for controlling evolution operators in metaheuristics have achieved significant popularity. In this survey, we focus on the research field itself and perform a bibliographical analysis to show how broad and active is nowadays the research field of chaos-enhanced metaheuristics and what are some of the most recent works published. [ABSTRACT FROM AUTHOR]

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial Neural Networks (DANN) are very popular in our days. Depending on the learning task, the exact form of DANNs is determined via their multi-layer architecture, activation functions and the so-called loss function. However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions. In the current paper, we suggest to analyze the neural signal processing in DANNs from the point of view of homogeneous chaos theory as known from polynomial chaos expansion (PCE). From the PCE perspective, the (linear) response on each node of a DANN could be seen as a 1st degree multi-variate polynomial of single neurons from the previous layer, i.e. linear weighted sum of monomials. From this point of view, the conventional DANN structure relies implicitly (but erroneously) on a Gaussian distribution of neural signals. Additionally, this view revels that by design DANNs do not necessarily fulfill any orthogonality or orthonormality condition for a majority of data-driven applications. Therefore, the prevailing handling of neural signals in DANNs could lead to redundant representation as any neural signal could contain some partial information from other neural signals. To tackle that challenge, we suggest to employ the data-driven generalization of PCE theory known as arbitrary polynomial chaos (aPC) to construct a corresponding multi-variate orthonormal representations on each node of a DANN. Doing so, we generalize the conventional structure of DANNs to Deep arbitrary polynomial chaos neural networks (DaPC NN). They decompose the neural signals that travel through the multi-layer structure by an adaptive construction of data-driven multi-variate orthonormal bases for each layer. Moreover, the introduced DaPC NN provides an opportunity to go beyond the linear weighted superposition of single neurons on each node. Inheriting fundamentals of PCE theory, the DaPC NN offers an additional possibility to account for high-order neural effects reflecting simultaneous interaction in multi-layer networks. Introducing the high-order weighted superposition on each node of the network mitigates the necessity to introduce non-linearity via activation functions and, hence, reduces the room for potential subjectivity in the modeling procedure. Although the current DaPC NN framework has no theoretical restrictions on the use of activation functions. The current paper also summarizes relevant properties of DaPC NNs inherited from aPC as analytical expressions for statistical quantities and sensitivity indexes on each node. We also offer an analytical form of partial derivatives that could be used in various training algorithms. Technically, DaPC NNs require similar training procedures as conventional DANNs, and all trained weights determine automatically the corresponding multi-variate data-driven orthonormal bases for all layers of DaPC NN. The paper makes use of three test cases to illustrate the performance of DaPC NN, comparing it with the performance of the conventional DANN and also with plain aPC expansion. Evidence of convergence over the training data size against validation data sets demonstrates that the DaPC NN outperforms the conventional DANN systematically. Overall, the suggested re-formulation of the kernel network structure in terms of homogeneous chaos theory is not limited to any particular architecture or any particular definition of the loss function. The DaPC NN Matlab Toolbox is available online and users are invited to adopt it for own needs. • Kernel structure reformulation of deep artificial neural networks in terms of homogeneous chaos theory. • Response on each node of the deep network represented through polynomial chaos expansion. • Orthonormal decomposition mitigates the non-optimal representation while processing the neural signal. • Accounting for high-order effects reflecting simultaneous neural impacts. • Analytical estimation of mean and variance of neural signal on each node is provided. [ABSTRACT FROM AUTHOR]

Objective To explore the chaotic dynamic mechanism of the formation and change of smoking behavior. Methods Based on the chaos theory, the chaotic characteristics of smoking-quitting behavior, the dynamic mechanism of chaotic process and chaos control strategy were analyzed by using typical analysis and comparative analysis. Results The formation and change of smoking habit accorded with the typical characteristics of chaos. The individual smoking behavior belief, which is composed of psychological cognition, behavioral motivation, and external environment/situation/occasion, is the aattractorn to induce and control the development, evolution, and disappearance of smoking behavior. The a scenario-motivationn coupling mechanism is the power source of smoking behavior, and multiple scenario-motivation, coupling mechanisms cooperate to dominate the behavior, which gradually increases the frequency of behavior and enters a chaotic state. The stability of chaotic system makes it difficult to quit the habit for a long time. Quitting smoking needs to fundamentally break the chaotic state of behavior and deconstruct multiple a scenario-motivation0 coupling mechanisms in chaotic attractors. Conclusion This study puts fonvard the chaotic dynamic mechanism of the formation and change of smoking habits, which provides a new perspective and train of thought for deeply understanding, explaining, and intervening other health-related behaviors and habits. It provides theoretical support for individual smoking cessation and smoking control policy-making. [ABSTRACT FROM AUTHOR]

Feature selection is a knowledge discovery tool to understand the problem by analysing features. In particular, the application of feature selection in data mining can not only improve the quality of extracted patterns and knowledge but also decrease computational costs. Various techniques have been applied to this complex optimization problem, in which metaheuristics have been validated to be superior. This study introduces a new metaheuristic known for having lean and fast programming, inspired by the sunflower's motions for feature selection for the first time. It is equipped with a v‐shaped transfer function and associated with the KNN classifier to become the binary sunflower optimization (BSFO). A total of 12 variants of BSFO are designed based on the chaos theory and Lévy flights, called improved binary sunflower optimization (IBSFO). A discussion between these improvement theories for feature selection has also not been made yet, and it is performed in this paper using 15 benchmark datasets from the UCI repository. The experimental results show that all variants can advance the fitness value of BSFO, and nine of them considerably decrease the computational costs. Furthermore, the chaotic BSFO with the Chebyshev function, taking replacement to normal rand, has the lowest fitness value (−11.37%) and execution time (−9.31%) than the original BSFO. Further, IBSFO is compared with another eight metaheuristics and outperforms these competitors on average fitness value and execution time. Overall, IBSFO proved to find subsets with reduced dimension and high accuracy with meagre computational cost due to its robust explorative and exploitative capacities. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel one-dimensional (1D) Sine–Tangent–Sine (STS) chaotic map. The proposed STS map exhibits a wider, continuous chaotic range, complex behaviour, and random distribution over the entire data range, when tested for bifurcation diagram, Lyapunov exponent and sample entropy parameters. The work also presents a novel video encryption scheme using the STS map. The proposed scheme mainly comprises three phases. In the first phase, the input video is split into frames, and a distinct S-box for each frame is generated using the STS map. In the second step, we perform the frame rotation followed by the shuffling of pixels within the frame. Dynamic diffusion is the final step that changes the value of pixels by selecting one of the chaotic maps, either Chebyshev map or proposed STS map, for each frame. The security analysis proves that the proposed map is resistant to various attacks. [ABSTRACT FROM AUTHOR]

The objective of this article is to characterize an aeroelastic system in terms of its dynamical behavior, which could be either chaotic or periodic before, during, and after achieving the flutter velocity. The aeroelastic system shown here is a wing with a high aspect ratio, which leads to a very flexible behavior subjected to unsteady flow. This paper compares the computational and experimental dynamical behavior of an aeroelastic system at the flutter velocity for the different dynamic stall models proposed. To understand the nonlinear behavior of this system, the traditional attractor reconstruction and Lyapunov exponent calculation are compared with the 0–1 test. In addition to this comparison, two dynamic stall semi-empirical models are applied directly to the time history. All these comparisons show that the computational and wind tunnel experiments are in good agreement, and the dynamic behavior usually gives close results for the 0–1 test and Lyapunov exponent. It is concluded that the system presents chaotic behavior when no dynamic stall correction is applied or when Gangwani's correction is applied. However, Boeing–Vertol's correction postpones the chaotic behavior, meaning that the chaotic behavior is only observed for velocities above the flutter. [ABSTRACT FROM AUTHOR]

This article discusses the utilisation of a Chua oscillator with a memristor to produce chaos with minimal nonlinearity. The memristor, a device that changes its flux or charges over time, has its nonlinear strength altered fractionally to determine the lowest-order memristor nonlinearity for generating chaos. An experimental analog circuit in real-time has been constructed. A linear parameter varying (LPV) approach, incorporating a suitable Lyapunov functional (LK) method, has been introduced to find new sufficient conditions for the robust stability of the resulting closed-loop system through linear matrix inequalities (LMIs). By observing the behaviour of the system without control, it is possible to understand the basic characteristics of chaotic oscillations and how they are affected by changes in the fractional order. These results can then be used as a starting point to study the effectiveness of various control techniques, such as feedback control, in reducing chaos and stabilising the system of this article. The efficiency of the cost-function-based control scheme is evaluated using the simulation results and relevant applications are addressed. [ABSTRACT FROM AUTHOR]

To study whether the free energy principle can explain fetal brain activity and the existence of fetal consciousness via a chaotic dimension derived using artificial intelligence. In this observational study, we used a four-dimensional ultrasound technique obtained to collect images of fetal faces from pregnancies at 27–37 weeks of gestation, between February and December 2021. We developed an artificial intelligence classifier that recognizes fetal facial expressions, which are thought to relate to fetal brain activity. We then applied the classifier to video files of facial images to generate each expression category's probabilities. We calculated the chaotic dimensions from the probability lists, and we created and investigated the free energy principle's mathematical model that was assumed to be linked to the chaotic dimension. We used a Mann–Whitney test, linear regression test, and one-way analysis of variance for statistical analysis. The chaotic dimension revealed that the fetus had dense and sparse states of brain activity, which fluctuated at a statistically significant level. The chaotic dimension and free energy were larger in the sparse state than in the dense state. The fluctuating free energy suggests consciousness seemed to exist in the fetus after 27 weeks. [ABSTRACT FROM AUTHOR]

For the chaotic motion control of a single-degree-of-freedom vibro-impact system with soft constraint, two-parameter cooperative intelligent optimal control method based on LRS-QPSO (i.e., Local Rotational Search Quantum Particle Swarm Optimization) algorithm optimization SVM (i.e., Support Vector Machines) was proposed. Firstly, in the parameter plane (ω,ζ), the motion distribution of the system and the change of the maximum Lyapunov exponent is obtained by numerical simulation, and the correlation between parameters change and the transition from chaotic motion to periodic motion is analyzed. Secondly, by introducing ω and ζ into the construction of the input variables of the SVM controller, a chaotic motion two-parameter cooperative intelligent optimal control strategy is proposed to meet the requirements of expected control objectives. Therefore, by the virtue of nonlinear mapping characteristics of SVM, the combined effects of ω and ζ on the dynamic state transition of the system can be reflected in the output variables of the controller. Finally, with single parameter ω and single parameter ζ as the research object, the bifurcation diagram, Lyapunov exponential spectrum, and controlled periodic motion orbit diagram are analyzed, and the advantages of two-parameter cooperative intelligent optimal control are compared and analyzed. [ABSTRACT FROM AUTHOR]

Coupling between modes is crucial for generating coherent structures and spatiotemporal chaos in optical systems. In an ultrafast fiber laser with birefringence, the stable pulse is viewed as a vector soliton (VS) with two orthogonal modes nonlinearly coupled through the Kerr effect and gain/loss. However, the dynamics of a VS in the presence of linear coupling is unperceived despite linear coupling playing a significant role in various optical systems. Here, it is shown that a local linear coupling between polarization modes in lasers facilitates brand‐new nonlinear states, including stationary, breathing, and chaotic VSs. The observed solitary states can be regarded as emergent phenomena when two particles (polarization modes) in a system have a simple interaction (linear coupling), which are ubiquitous in biology, chemistry, and complex systems. It is found that linear coupling is essential for sustaining the internal balance between two modes within the VS. Chaotic dynamics of VS emerge under weak linear coupling, while the two modes lose trapping due to the birefringence in the absence of linear coupling. This work can offer new insight into the two‐mode nonlinear system and inspire research interests in the intelligent manipulation of ultrashort pulse lasers. [ABSTRACT FROM AUTHOR]

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi–Yau geometries, as well as some nonrelativistic models. We find that for the Calabi–Yau models, the Lanczos coefficients grow slower than linearly for small n 's, consistent with the behavior of integrable models. On the other hand, for the nonrelativistic models, the Lanczos coefficients initially grow linearly for small n 's, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope. [ABSTRACT FROM AUTHOR]

Introduction: In the aging process of the body, in addition to changes in fat and muscle content, there is also bone loss, implying the possibility of a strong muscle–bone–lipid link. In this study, we initially investigated the relationship between lumbar BMD and low muscle mass and the relationship between "muscle–bone–lipid." Methods: The datasets from the National Health and Nutrition Examination Survey (NHANES) 2011–2018 were used in a cross-sectional investigation. BMD and appendicular skeletal muscle (ASM) were measured by dual-energy X-ray absorptiometry (DXA), and appendicular skeletal muscle was adjusted by body mass index (BMI) as a marker of sarcopenia. Weighted multivariate regression and logistic regression analysis were used to explore the independent relationship between lumbar BMD and sarcopenia. Fitted smoothing curves and threshold effect analysis were used to describe the nonlinear relationship. Result: In 8386 participants with ages 20–59 years, there was a negative association between lumbar BMD and sarcopenia. In the fully adjusted model, the risk of developing sarcopenia decreased by 93% for each 1-unit increase in lumbar BMD (OR = 0.07, 95%CI 0.03–0.20). The risk of sarcopenia was 58% lower in participants in the highest quartile of lumbar BMD than in those in the lowest quartile (OR = 0.42, 95%CI 0.27–0.64). This negative association was more pronounced in the population of women with BMI ≥ 25. Conclusion: Our findings suggest that lumbar BMD is negatively associated with sarcopenia in US adults. The dynamic balance between "muscle–bone–lipid" is likely to be related to the pathogenesis of bone loss. [ABSTRACT FROM AUTHOR]

This paper introduces a new three-dimensional chaos system that is different from any existing chaotic systems. The basic dynamic properties of the suggested system have been analyzed through theoretical and numerical studies and the rich chaotic behavior has been confirmed using phase portraits, Lyapunov analysis and bifurcation diagram. A simple model with a nonlinear quadratic term, unstable saddle equilibrium points and broadband chaotic behavior are some of the interesting features of the suggested system. Then, due to higher accuracy of fractional order models than integer order models, a novel fractional chaotic system has been extracted based on the suggested chaotic system and new nonlinear methods planned to achieve the synchronization and anti-synchronization goals for the system. A backstepping approach is designed to synchronize and ensure stability in Lyapunov's concept. Also, the anti-synchronization between the two novel fractional systems is achieved by applying the active control technique, and subsequently Lyapunov stability is shown under the proposed scheme. The simulation results in MATLAB environment show the synchronization and anti-synchronization efficiency for the proposed innovative fractional order turbulent system. [ABSTRACT FROM AUTHOR]

In this paper, the abundant nonlinear dynamical behaviors of a fractional-order time-delayed Duffing system under harmonic excitation are studied. By constructing Melnikov function, the necessary conditions of chaotic motion in horseshoe shape are detected, and the chaos threshold curve is obtained by comparing the results obtained through the Melnikov theory and numerical iterative algorithm. The results show that the trend of change is the same, which confirms the accuracy of the chaos threshold curve. It could be found that when the excitation frequency ω is larger than a certain value, the Melnikov theory is not valid for these values. Furthermore, by numerical simulation, some numerical results are obtained, including phase portraits, the largest Lyapunov exponents, and the bifurcation diagrams, Poincare maps, time histories, and frequency spectrograms at some typical points. These numerical simulation results show that the system exhibits some new complex dynamical behaviors, including entry into the state of chaotic motion from single period to period-doubling bifurcation and chaotic motion and periodic motion alternating under the necessary condition of chaotic occurrence. In addition, the effects of time delay, fractional-order coefficient, fractional order, linear viscous damping coefficient, and linear stiffness coefficient on the chaotic threshold curve are discussed, respectively. Those results reveal that there exist abundant nonlinear dynamic behaviors in this fractional-order system, and by adjusting these parameters reasonably, the system could be transformed from chaotic motion to non-chaotic motion. [ABSTRACT FROM AUTHOR]

Further exploration into the influence of a memristor on the behavior of chaotic systems deserves attention. When constructing memristor chaotic systems, it is commonly believed that increasing the number of memristors will lead to better system performance. This paper proposes a class of chaotic maps with different discrete memristors, achieved through internal perturbation based on the Sine map. The I-V curve of the discrete memristor has a symmetrical structure. The dynamic characteristics of the designed system are analyzed using the chaotic attractor phase diagram, Lyapunov exponent (LE) spectrum, and bifurcation diagram. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map's chaotic characteristics, expand the chaos range, and improve the ergodicity and LE value. Moreover, the type of discrete memristors has a significant impact on the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, in this paper, a direction for the design of a discrete memristor chaotic system is provided. Finally, a discrete memristor chaotic map with a simple structure and better performance is selected. Based on this, a pseudo-random sequence generator is designed, and the generated sequence passes the National Institute of Standards and Technology (NIST) test. [ABSTRACT FROM AUTHOR]

The Brinkman–Bénard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number,  R a c , and the wave number,  a c , are obtained in closed form. An asymptotic analysis is performed, to obtain  R a c  for the case of adiabatic boundaries, for which  a c ≃ 0 . A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the Hopf–Rayleigh number are, however, opposite to each other. In view of the known analogy between Bénard convection and Taylor–Couette flow in the linear regime, it is imperative that the results of the latter problem, viz., Brinkman–Taylor–Couette flow, become as well known. [ABSTRACT FROM AUTHOR]

Swarm robotics can cooperatively perform large, multiple tasks by controlling a swarm composed of many robots. Currently, approaches for operating multiple robot swarms are being studied for further evolution of this system. This study addresses a multiple movement task in which robot swarms move collectively in the same environment. In this task, the movement paths of robot swarms must pass each other in a cooperative manner when they intersect. The robots in this system behave under autonomous distributed control, thus must consider a passing behavior suitable for their own situation. This study proposes a turning behavior based on the chaos theory to ensure that a robot swarm avoids other approaching robot swarms. Each robot swarm applying the proposed method passes other swarms while autonomously deciding its turning direction and continuing its own collective movement task. In addition, the decision making based on the chaos theory predicts future values according to the current value. Therefore, it is expected to be useful for task scheduling. The performance of multiple robots passing each other is evaluated with the proposed method using numerical simulations. This performance shows that the robot swarms can avoid each other without collision using the closest inter-robot distance as the evaluation metric. Finally, robot swarms with varying shapes and scales complete their own movements in an environment where these movement paths intersect at a single point. [ABSTRACT FROM AUTHOR]

This review presents an overview of Lorenz models between 1960 and 2008, classified into six categories based on different types of Partial Differential Equations (PDEs). These models have made significant contributions to our understanding of chaos, the butterfly effect, attractor coexistence, and intransitivity (or "almost intransitivity") across various scientific fields. Type I models include the influential Lorenz 1963 model and generalized Lorenz models. The classical Lorenz model laid the groundwork for chaos theory by revealing the sensitivity to initial conditions and chaotic behavior. Generalized Lorenz models were developed to examine the dependence of chaos on the number of Fourier modes and to illustrate attractor coexistence. Type II models were derived from two-layer, quasi-geostrophic systems. These models investigated nonlinear oscillations and irregular solutions. Based on these models, in 1960, Lorenz first presented nonperiodic solutions. Type III models include the Lorenz 1960 and 1969 models, derived from a vorticity-conserved PDE. These models shed light on nonlinear oscillatory solutions, linearly unstable solutions, and the predictability estimates of the atmosphere. However, recent studies have raised doubts regarding the validity of the two-week predictability limit. Type IV models, based on shallow water equations, have advanced our understanding of the coexistence of slow and fast variables. Type V models, which include models not based on specific PDEs, include the Lorenz 1984 and 1996 models used for studying intransitivity and investigating data assimilation techniques. Type VI models, involving difference equations, have proven effective in demonstrating chaos and intransitivity across diverse fields. Interestingly, Lorenz's early work in 1964 and 1969 employed the Logistic map, appearing earlier than significant studies in the 1970s. In summary, the study of Lorenz models has deepened our understanding of chaos, attractor coexistence, and intransitivity (or "almost intransitivity"). Future research directions may involve exploring higher-dimensional models, utilizing advanced mathematical and computational techniques, and fostering interdisciplinary collaborations to further advance our comprehension and the prediction of capabilities regarding coexisting chaotic and nonchaotic phenomena, as well as regime changes. [ABSTRACT FROM AUTHOR]

This paper analytically and numerically investigates the dynamical characteristics of a fractional Duffing–van der Pol oscillator with two periodic excitations and the distributed time delay. First, we consider the pitchfork bifurcation of the system driven by both a high-frequency parametric excitation and a low-frequency external excitation. Utilizing the method of direct partition of motion, the original system is transformed into an effective integer-order slow system, and the supercritical and subcritical pitchfork bifurcations are observed in this case. Then, we study the chaotic behavior of the system when the two excitation frequencies are equal. The necessary condition for the existence of the horseshoe chaos from the homoclinic bifurcation is obtained based on the Melnikov method. Besides, the parameters effects on the routes to chaos of the system are detected by bifurcation diagrams, largest Lyapunov exponents, phase portraits, and Poincaré maps. It has been confirmed that the theoretical predictions achieve a high coincidence with the numerical results. The techniques in this paper can be applied to explore the underlying bifurcation and chaotic dynamics of fractional-order models. [ABSTRACT FROM AUTHOR]

We study a system of four identical globally coupled phase oscillators with a biharmonic coupling function. Its dimension and the type of coupling make it the minimal system of Kuramoto-type (both in the sense of the phase space's dimension and the number of harmonics) that supports chaotic dynamics. However, to the best of our knowledge, there is still no numerical evidence for the existence of chaos in this system. The dynamics of such systems is tightly connected with the action of the symmetry group on its phase space. The presence of symmetries might lead to an emergence of chaos due to scenarios involving specific heteroclinic cycles. We suggest an approach for searching such heteroclinic cycles and showcase first examples of chaos in this system found by using this approach. [ABSTRACT FROM AUTHOR]

The Chaos Game Optimization (CGO) has only recently gained popularity, but its effective searching capabilities have a lot of potential for addressing single-objective optimization issues. Despite its advantages, this method can only tackle problems formulated with one objective. The multi-objective CGO proposed in this study is utilized to handle the problems with several objectives (MOCGO). In MOCGO, Pareto-optimal solutions are stored in a fixed-sized external archive. In addition, the leader selection functionality needed to carry out multi-objective optimization has been included in CGO. The technique is also applied to eight real-world engineering design challenges with multiple objectives. The MOCGO algorithm uses several mathematical models in chaos theory and fractals inherited from CGO. This algorithm's performance is evaluated using seventeen case studies, such as CEC-09, ZDT, and DTLZ. Six well-known multi-objective algorithms are compared with MOCGO using four different performance metrics. The results demonstrate that the suggested method is better than existing ones. These Pareto-optimal solutions show excellent convergence and coverage. [ABSTRACT FROM AUTHOR]

In this paper, we compare three energy harvesting systems in which we introduce additional bumpers whose mathematical model is mapped with a non-linear characteristic based on the hyperbolic sine Fibonacci function. For the analysis, we construct non-linear two-well, three-well and four-well systems with a cantilever beam and permanent magnets. In order to compare the effectiveness of the systems, we assume comparable distances between local minima of external wells and the maximum heights of potential barriers. Based on the derived dimensionless models of the systems, we perform simulations of non-linear dynamics in a wide spectrum of frequencies to search for chaotic and periodic motion zones of the systems. We present the issue of the occurrence of transient chaos in the analyzed systems. In the second part of this work, we determine and compare the effectiveness of the tested structures depending on the characteristics of the bumpers and an external excitation whose dynamics are described by the harmonic function, and find the best solutions from the point view of energy harvesting. The most effective impact of the use of bumpers can be observed when dealing with systems described by potential with deep external wells. In addition, the use of the Fibonacci hyperbolic sine is a simple and effective numerical tool for mapping non-linear properties of such motion limiters in energy harvesting systems. [ABSTRACT FROM AUTHOR]

The practical applications of chaotic systems are gaining more dimensions every day. In this paper, a new 3D chaotic system is presented with three nonlinear terms and unique strong chaotic behavior. For the initial evaluation of the behavior of the innovative chaotic system, analyses related to equilibrium points, sensitivity, stability, Lyapunov exponent, and bifurcation have been carried out, and its strong attractor manner has been well shown. The practical realization of the designed system is shown by its circuit implementation through the use of electronic elements and Kirchhoff's laws. To show the performance of the innovative system in practical applications, first a synchronization technique inspired by non-linear and active approaches has been designed, and then by using the innovative chaotic system in the masking technique, a new information encryption method has been derived. The results obtained from the masking based on the innovative chaotic system and the designed synchronization technique show the high functionality of the derivative encryption method. [ABSTRACT FROM AUTHOR]

In recent years, many studies have been used in feed-forward neural network (FNN) to develop decision-making systems. The primary objective is to get the least error by finding the best combination of control parameters. It has been observed that FNNs using meta-heuristics techniques always converges very quickly towards the optimal positions but suffers from slow searching speeds at later stages of generation. Due to slow convergence, it is a prevalent phenomenon that traditional optimization does not ensure to find global optima. As a result, it falls under local optima. Recently, another meta-heuristic optimization-based algorithm called sine cosine algorithms (SCA) was introduced to solve the aforementioned issues. The algorithm is fundamentally predicated on two trigonometric functions, one being sine and the other being cosine. However, like other traditional approaches, SCA has a tendency to be stuck in sub-optimal regions due to poor exploration and exploitation capabilities. This paper proposes an improved version of SCA named chaotic oppositional SCA (COSCA) by integrating with chaos theory and oppositional based learning into the SCA optimization process. It is an incipient training method employed to train an FNN. Three benchmark problems are used to examine the precision and performance of FNNs equipped with COSCA, COPSO, OSCA, SCA, PSO, and backpropagation. The experimental results showed that, relative to other meta-heuristic optimization techniques, the COSCA technique is able to improve performance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the unwanted chaotic oscillation that can severely affect the reliable and safe operation of electrical power systems. The dynamical behavior of a benchmark three-bus nonlinear electrical power system model is explored using modern nonlinear analysis methods, where the Lyapunov exponents spectrum, bifurcation diagram, power spectral density and bicoherence are used to investigate the chaotic oscillation in the power system. The analysis shows the existence of critical parameter values that may drive the power system to an unstable region and can expose the system to bus voltage collapse and angle divergence or blackout. To eliminate the chaotic oscillation, a fractional-order fixed time sliding mode controller has been used to control the power system in a finite time that can be predetermined by the designer. The Lyapunov theorem has been used to prove the stability of the controlled power system. The results confirm the superiority, robustness, and effectiveness of the suggested control algorithm. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby. [ABSTRACT FROM AUTHOR]

The main theme of this work corresponds to the relationship between entropy and chaos theory, to explain through logical argumentation that the reality of society is a dissipative structure that manifests itself through chaotic components. This project arises from the concept of entropy (second law of thermodynamics) as a quantity that determines the irreversibility of a process and the concept that explains the cause of natural transformation, tending to a permanent increase in the universe, which underlies the degradation of systems and convergence towards chaos. As a hermeneutical instrument to interpret social interaction, this paper uses mathematical logic framed in a philosophical context through hermeneutics as an argumentation tool; seeking to describe the logical construction of social interaction as a dissipative entity with the constant entropic increase of nature. [ABSTRACT FROM AUTHOR]

• Constructing pseudo-Hamiltonian system, the topology of dynamic motion is able to distinguish whether the system is in chaos. • The fractal process of the attraction basin verifies the chaotic distribution solved by Melnikov function. • Larger force fluctuation leads to the critical point hysteresis of damping and average force occurring bifurcation or chaos. • The quantitative optimal couple of structural with process parameters determine the priority of the parameter control. This paper investigates the stability of horizontal nonlinear vibration of four-high cold mill under the effects of gyro-precession and eccentricity between rolls. The threshold value of chaos about Smale horseshoe commutation is given from Melnikov method, and the correctness of the result is verified by the fractal process of the attraction basin. Through the analyzes of bifurcation, maximum Lyapunov exponents and bi-parameter bifurcation, it is revealed for the effect of different parameters variation on the nonlinear dynamic behavior of horizontal vibration in rolling system. The results show, the fluctuation amplitude of horizontal force increases, the stable domain decreases, and once its value ≥3.5, it is necessary to prefer to the adjustment of parameter-exciting stiffness; meanwhile, it is noticeable that the critical points of damping and average force of the system with bifurcation or chaos appear hysteresis. The evolutions of system dynamics with four pairs of parameter changes confirm the quantitative optimal couple of one structural plus one process parameter in the system. Based on this, we can also find a balance between the average horizontal force and eccentricity, so as to optimize the structural design so that there is a proper and reliable eccentricity between the rolls. The results provide a theoretical reference for service stability and dynamic reliability of the rolling mill system. [ABSTRACT FROM AUTHOR]

This work investigates the bifurcation analysis in a discrete-time Leslie–Gower predator–prey model with constant yield predator harvesting. The stability analysis for the fixed points of the discretized model is shown briefly. In this study, the model undergoes codimension-1 bifurcation such as fold bifurcation (limit point), flip bifurcation (period-doubling) and Neimark–Sacker bifurcation at a positive fixed point. Further, the model exhibits codimension-2 bifurcations, including Bogdanov–Takens bifurcation and generalized flip bifurcation at the fixed point. For each bifurcation, by using the critical normal form coefficient method, various critical states are calculated. To validate our analytical findings, the bifurcation curves of fixed points are drawn by using MATCONTM. The system exhibits interesting rich dynamics including limit cycles and chaos. Moreover, it has been shown that the predator harvesting may control the chaos in the system. [ABSTRACT FROM AUTHOR]

This paper proposes a new one-dimensional chaotic map—nonlinear coupled Sine-Tent-Logistic chaotic map (1DNCSTL). A series of tests on this map show that the map has the characteristics of randomness and sensitivity to initial values and is suitable for image encryption. Based on this map, the article further proposes pixel bit position scrambling and reorganization operation and dynamic nonunique diffusion operation. Pixel bit position scrambling and reorganization operation is different from the traditional scrambling operation that only changes the position of the pixel value; this operation can achieve the effect of changing the pixel position and pixel value at the same time. The dynamic nonunique diffusion operation is different from the traditional unique-formula diffusion operation. The diffusion formula is not unique, which can ensure the security of the algorithm. Simulation experiment results and various security performance analysis show that the algorithm proposed in this paper has good performance. Compared with other encryption schemes, this algorithm is more suitable for image encryption. [ABSTRACT FROM AUTHOR]

This paper presents the results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior. Numerical results using phase portraits, bifurcation diagrams, Lyapunov exponents, and 0-1 testing confirmed chaotic and hyperchaotic behavior. The results also proved the effectiveness of the control, showing errors below 1%, even in cases where the control design is subject to parametric errors. Additionally, an investigation of the system in fractional order is included, demonstrating that the system has periodic, constant, or chaotic behavior for specific values of the order of the derivative. [ABSTRACT FROM AUTHOR]

A chaotic oscillator has been designed based on a Sallen Key-type high-pass filter (HPF). The HPF has been converted to a chaotic oscillator using a parallel combination of a PN junction diode as a nonlinear element and an inductor as an energy storage element. The dynamics of the proposed system has been simulated numerically using fourth-order Runge–Kutta method. The circuit exhibits period-doubling route to chaos as well as period-adding route to chaos depending on the choice of system parameters. Striking features like antimonotonicity and coexistence of attractors are also observed. Bifurcation diagram, phase plane plots and spectrum of Lyapunov exponents have been employed to describe the chaotic behavior of the system. A hardware experiment has been carried out to verify the same in the laboratory using off-the-shelf components. [ABSTRACT FROM AUTHOR]

Theoretically, an eight-term chaos system is presented. The effect of changing the initial conditions values on behavior Chen system was studied. The basic dynamical properties of system are analyzed like time series, attractor, FFT spectrum, and bifurcation. Where the system appears steady state behavior at initial condition xi, yi, zi equal (0, 0, 0) respectively and it convert to quasi-chaotic at xi,yi,zi equal (-0.1, 0.5,-0.6). Finally, the system become hyper chaotic at xi,yi, zi equal(- 0.5, 0.5,-0.6 ) that can used it in many applications like secure communication. [ABSTRACT FROM AUTHOR]

In this work, we present multiple variations of the Multi-verse Optimizer Algorithm (MVO) using chaotic maps, using it in the formation of new solutions. In these new variations of the MVO algorithm, which we call the Fuzzy-Chaotic Multi-verse Optimizer (FCMVO), we use multiple chaotic maps used in the literature to substitute some of the parameters for which the original algorithm used a random value in the formation of new universes or solutions. To implement chaos theory on these new variants, we also use Fuzzy Logic for dynamic parameter adaptation; the first tests are performed only using chaotic maps, and then we merge the use of Fuzzy Logic in each of these cases to analyze the improvement over the Fuzzy MVO. Subsequently, we use only the best-performing chaos maps in a new set of variants for the same cases; after these results, we observe the behavior of the algorithm in different cases. The objective of this study is to compare whether there is a significant improvement over the MVO algorithm using some of the best-performing chaotic maps in conjunction with Fuzzy Logic in benchmark mathematical functions prior to moving on to other case studies. [ABSTRACT FROM AUTHOR]

Employing the Riccati–Bernoulli sub-ODE method (RBSM) and improved Weierstrass elliptic function method, we handle the proposed (2 + 1) -dimensional nonlinear fractional electrical transmission line equation (NFETLE) system in this paper. An infinite sequence of solutions and Weierstrass elliptic function solutions may be obtained through solving the NFETLE. These new exact and solitary wave solutions are derived in the forms of trigonometric function, Weierstrass elliptic function and hyperbolic function. The graphs of soliton solutions of the NFETLE describe the dynamics of the solutions in the figures. We also discuss elaborately the effects of fraction and arbitrary parameters on a part of obtained soliton solutions which are presented graphically. Moreover, we also draw meaningful conclusions via a comparison of our partially explored areas with other different fractional derivatives. From our perspectives, by rewriting the equation as Hamiltonian system, we study the phase portrait and bifurcation of the system about NFETLE and we also for the first time discuss sensitivity of the system and chaotic behaviors. To our best knowledge, we discover a variety of new solutions that have not been reported in existing articles V 1 , 2 ∗ ∗ , ... , V 7 , 8 ∗ ∗ , V 9 , 1 0 , ... , V 1 3 , 1 4 . The most important thing is that there are iterative ideas in finding the solution process, which have not been seen before from relevant articles such as [Tala-Tebue et al., 2014; Fendzi-Donfack et al., 2018; Ashraf et al., 2022; Ndzana et al., 2022; Halidou et al., 2022] in seeking for exact solutions about NFETLE. [ABSTRACT FROM AUTHOR]