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Chaos theory offers a unique lens to understand the intricate relationships between economic growth and energy supply pricing. Existing economic theories often emphasize energy prices' inherent randomness, unpredictability, and economic growth. A deeper comprehension can be achieved by applying chaos theory to this complex system. Developing a dynamic model that captures the causal relationships among the various variables impacting economic growth, energy supply, and pricing is crucial for unraveling this complexity. This study aims to delve into the chaotic nature of the energy economy system within the context of economic growth. The research methodology is rooted in a fundamental-applied approach. By employing numerical simulation techniques, specifically utilizing the Simulink MATLAB toolbox, the study seeks to explore and potentially control chaos within the system. The findings highlight the system's nonlinear dynamics, showcasing its sensitivity to initial conditions and exhibiting chaotic behavior, limit cycles, and stable equilibrium points across varying initial values. This research endeavor contributes to a more nuanced understanding of the interplay between energy economics, economic growth, and pricing dynamics.

Chronic myalgias and arthralgias occur after Chikungunya virus infections (pCHIKV- M&A). We report details of treating a 6-years lasting CHIKV-M&A pains with a combination of medications and interventions. The patient had severe pain in bilateral shoulders and elbows; right thumb and back. Response to steroids, sulphasalazine and methotrexate was poor. Examination revealed M&A pains. Medications initiated included Pregabalin, Paracetamol, Tramadol and vitamin D. At two weeks, despite improvement, there were residual pains in bilateral shoulders and elbows. Four weekly sessions (two on each side), of ultrasound-guided dry needling (USGDN) of all muscles of the upper limb was done. Patient reassessment revealed moderate, residual pains at bilateral supraspinatus muscles, bicipital tendons and radio-humeral joints. These pains were addressed by USG guided steroid injection of bilateral- suprascapular nerves, bicipital tendons and radio-humeral joints. Medications reduced pains especially of back and thumb. USGDN of muscles further reduced it by 60%. The interventions at the nerves, entheses and joints gave 90%-100% relief. The pre-intervention Disability of Arm, Shoulder and Hand (DASH) score of 52.7 reduced to 5.4. At fifth month follow-up, the DASH was15.8, but patient reported satisfaction over pain relief, improvement in daily activities and quality-of-life. There are no evidence-based treatment guidelines or corroborative evidence for rheumatic pathology (most times) for persistent CHIKV-M&A pains. This case-report highlights the successful management of CHIKV-M&A pains by multi-modal approach. USGDN and steroids have neuro-modulatory effects. We have proposed that USGDN aids pain relief by an integrative role with the biologically inherent “chaos theory.”

Abstract One of the biggest problems with Internet of Things (IoT) applications in the real world is ensuring data integrity. This problem becomes increasingly significant as IoT expands quickly across a variety of industries. This study presents a brand-new data integrity methodology for Internet of Things applications. The “sequence sharing” and “data exchange” stages of the suggested protocol are divided into two parts. During the first phase, each pair of nodes uses a new chaotic model for securely exchanging their identity information to generate a common sequence. This phase’s objectives include user authentication and timing calculations for the second phase of the recommended method’s packet validation phase. The recommended approach was tested in numerous settings, and various analyses were taken into account to guarantee its effectiveness. Also, the results were compared with the conventional data integrity control protocol of IoT. According to the results, the proposed method is an efficient and cost-effective integrity-ensuring mechanism with eliminates the need for third-party auditors and leads to reducing energy consumption and packet overhead. The results also show that the suggested approach is safe against a variety of threats and may be used as a successful integrity control mechanism in practical applications.

Chaos identification can not only promote the development and perfection of chaos theory, but also help to find the factors that produce chaos in the considered system, and control or anti-control it. The 0–1 test for chaos is an effective method to detect chaos. In order to simulate the noise contaminated through its production, Gaussian, Exponential, and Uniform noises are added to Logistic mapping to form a new hybrid time series, respectively. The effects of noise types and levels on the modified 0–1 test for chaos are studied. By studying the effect of different types of noises on chaos index D c ∗ (n) , K corr ∗ (c) , and the change of K m.corr ∗ (c) with amplitude α , it can be seen that Uniform noise has the greatest effect on chaos identification. In addition, it is found that the effect of the noise types on chaos identification depends on the peak of the noisy time series, and the effect of the noise on chaos detection increases with the increase of the noisy time series peak. It is worth noting that the selection of amplitude α can improve the noise resistance of chaos identification. The noise resistance of the modified 0–1 test for chaos can be improved by adjusting the amplitude α of the parameters. With the continuous increase of noise contamination level, the effect on the modified 0–1 test for chaos detection results is gradually enhanced, so reducing the noise contamination level is the key to improving the accuracy of the modified 0–1 test for chaos. In addition, adjusting the amplitude α can also play a certain noise immunity effect, and when α = 2 , the noise immunity is stronger on logistic mapping. Sample size N up to 2 0 0 0 is sufficient, but amplitude ω has little effect on chaos identification. [ABSTRACT FROM AUTHOR]

As a nonlinear dynamic system, the dynamic equation of triboelectric nanogenerator system is not only difficult to accurately establish, but also difficult to solve. The output signals of triboelectric nanogenerator system depends on the initial conditions of the system, which reflects the dynamic behavior of the system. Currently, there is little research on using the output signals to study the dynamic behavior of triboelectric nanogenerator system. Therefore, a dynamic simulation model of a freestanding triboelectric nanogenerator (F-TENG) system was established using COMSOL software. The mathematical model of the F-TENG system was fitted. Using chaos theory and its phase-space reconstruction technology, the phase-space trajectories of the F-TENG system were reconstructed through voltage signals under external factors, and the dynamic behavior of the F-TENG system was discussed and studied. Finally, validation experiments were carried out. The research shows that with the variation of internal factors and operating frequency, the mathematical model of the F-TENG system remains basically unchanged, and the variation law of output characteristics also remains basically unchanged. The F-TENG system is in periodic motion; with the variation of external factors such as resistance and friction layer spacing, the mathematical model of the F-TENG system will evolve in a complex direction, and the output characteristics will gradually distort. The F-TENG system will evolve from periodic motion to chaotic motion. The research results not only reveal the dynamic behavior and enrich the nonlinear dynamic theory of triboelectric nanogenerator system, but also provide theoretical guidance for increasing the working bandwidth and stability of triboelectric nanogenerator system. [ABSTRACT FROM AUTHOR]

In this paper, the qualitative properties of a physically extended six-dimensional Lorenz system, with additional physical terms describing rotation and density, which was proposed in [Moon et al., 2019] have been investigated. The dissipation, invariance, Lyapunov exponents, Kaplan–Yorke dimension, ultimate boundedness and global attractivity of this six-dimensional Lorenz system have been discussed in detail according to the chaotic systems theory. We find that this system exhibits chaos phenomena for a new set of parameters. It is well known that the general method for studying the bounds of a chaotic system is to construct a suitable Lyapunov-like function (or the generalized positive definite and radically unbounded Lyapunov function). However, the higher the dimension of a chaotic system, the more difficult it is to construct the Lyapunov-like function. The innovation of this paper is that we first construct the suitable Lyapunov-like function for this six-dimensional Lorenz system, and then we prove that this system is not only globally bounded for varying parameters, but it also gives a collection of global absorbing sets for this system with respect to all parameters of this system according to Lyapunov's direct method and the optimization method. Furthermore, we obtain the rate of the trajectories going from the exterior to the global absorbing set. Some numerical simulations are presented to validate our research results. Finally, we give a direct application of the results obtained in this paper. According to the results of this paper, we can conclude that the equilibrium point O (0 , 0 , 0 , 0 , 0 , 0) of this system is globally exponentially stable. [ABSTRACT FROM AUTHOR]

Background The optimal dosing strategy for rifampicin in treating drug-susceptible tuberculosis (TB) is still highly debated. In the phase 3 clinical trial Study 31/ACTG 5349 (NCT02410772), all participants in the control regimen arm received 600 mg rifampicin daily as a flat dose. Here, we evaluated relationships between rifampicin exposure and efficacy and safety outcomes. Methods We analyzed rifampicin concentration time profiles using population nonlinear mixed-effects models. We compared simulated rifampicin exposure from flat- and weight-banded dosing. We evaluated the effect of rifampicin exposure on stable culture conversion at 6 months; TB-related unfavorable outcomes at 9, 12, and 18 months using Cox proportional hazard models; and all trial-defined safety outcomes using logistic regression. Results Our model-derived rifampicin exposure ranged from 4.57 mg · h/L to 140.0 mg · h/L with a median of 41.8 mg · h/L. Pharmacokinetic simulations demonstrated that flat-dosed rifampicin provided exposure coverage similar to the weight-banded dose. Exposure-efficacy analysis (n = 680) showed that participants with rifampicin exposure below the median experienced similar hazards of stable culture conversion and TB-related unfavorable outcomes compared with those with exposure above the median. Exposure-safety analysis (n = 722) showed that increased rifampicin exposure was not associated with increased grade 3 or higher adverse events or serious adverse events. Conclusions Flat-dosing of rifampicin at 600 mg daily may be a reasonable alternative to the incumbent weight-banded dosing strategy for the standard-of-care 6-month regimen. Future research should assess the optimal dosing strategy for rifampicin, at doses higher than the current recommendation. [ABSTRACT FROM AUTHOR]

One technique, especially in chaos-based cryptographic applications, is to include the message in the evolution of the dynamical system. This paper aims to find out if and to what extent the statistical behavior of the chaotic system is affected by the message inclusion in its dynamic evolution. The study is illustrated by the dynamical system described by the logistic map in cryptographic applications based on images. The evaluation of the statistical behavior was performed on an original scheme proposed. The Monte Carlo analysis of the applied Kolmogorov–Smirnov statistical test revealed that the dynamical system in the processing scheme with message inclusion does not modify its proper statistical behavior (revealed by definition relation). This was possible due to the proposed scheme designed. Namely, this scheme contains a decision switch which, supported by an appropriate choice of the magnitude of the scaling factor, ensures that the values of the dynamical system are maintained in the definition domain. The proposed framework for analyzing the statistical properties and for preserving the dynamical system behavior is one main contribution of this research. The message inclusion scheme also provides an enhancement with cryptographic mixing functions applied internally; the statistical behavior of the dynamical system is also analyzed in this case. Thus, the paper contributes to the theoretical complex characterization of the dynamical system considering also the message inclusion case. [ABSTRACT FROM AUTHOR]

One of the routine exercises to manage and improve the performance and utility of the cloud is the migration or transfer of cloud data whether it is large or small. However, it is extremely challenging to protect both data privacy and integrity concurrently while moving cloud data, particularly when it is very vast. Collectively, prior works fail to offer a complete solution to these problem. Even though data encryption and steganography techniques are popular and efficient, they provide higher time and space complexities and introduce information loss. As a result, the goal of this research is to provide a chaos compression and encryption system based on chaos theory to guarantee both data privacy and integrity during the transit or migration of massive cloud data. During data transmission, the entire data are compressed using a chaotic substitution box followed by an adaptive Huffman encoding algorithms. Therefore, the input data are efficiently transformed into a non-readable form which replaces the original data, making it difficult for an unethical individual or group to determine its true sense. Our evaluation results show that the proposed chaotic technique has a maximum entropy value of 7.99, which supports its ability to provide more privacy when compared to previous techniques. It also delivers the best bits per code of 4.41, a throughput of 2.89 MB/s, and a minimal information loss percentage of 0.0011%, demonstrating its superior time, space efficiency, and ability to improve data integrity over existing methods. [ABSTRACT FROM AUTHOR]

In the humanitarian assistance sector, the primary objective of inter-organizational networks is to ensure that there are efficient and effective humanitarian response efforts that meet the needs of the affected population to the maximum extent possible (Drabek, 1987; Zhao et al., 2009). However, theoretical perspectives on humanitarian organizational networks and effective disaster response have remained relatively modest and confined to developing basic typologies of coordination arrangements and identifying the challenges encountered in the disaster management process. (Bennett, 1999) There also seems to be limited academic endeavor to use network, complexity, chaos and systems theories for disaster research not only for large-scale emergencies worldwide but also in developing countries. Most research works concentrate on an approach limited to a much smaller scale of nodes (organizational actors). In the preceding section, a review of relevant theories is presented in the context of humanitarian organizational network and disaster response. [ABSTRACT FROM AUTHOR]

Physiological phenomena exhibit complex behaviours arising at multiple time scales. To investigate them, techniques derived from chaos theory were applied to physiological signals, providing promising results in distinguishing between healthy and pathological states. Fractal-like properties of electrodermal activity (EDA), a well-validated tool for monitoring the autonomic nervous system state, have been reported in previous literature. This study proposes the multiscale complexity index of electrodermal activity ( M C o m E D A ) to discern different autonomic responses based on EDA signals. This method builds upon our previously proposed algorithm, C o m E D A , and it is empowered with a coarse-graining procedure to provide a view at multiple time scales of the EDA response. We tested M C o m E D A 's performance on the EDA signals of two publicly available datasets, i.e., the Continuously Annotated Signals of Emotion (CASE) dataset and the Affect, Personality and Mood Research on Individuals and Groups (AMIGOS) dataset, both containing physiological data recorded from healthy participants during the view of ultra-short emotional video clips. Our results highlighted that the values of M C o m E D A were significantly different (p-value < 0.05 after Wilcoxon signed rank test with Bonferroni's correction) when comparing high- and low-arousal stimuli. Furthermore, M C o m E D A outperformed the single-scale approach in discriminating among different valence levels of high-arousal stimuli, e.g., showing significantly different values for scary and amusing stimuli (p-value = 0.024). These findings suggest that a multiscale approach to the nonlinear analysis of EDA signals can improve the information gathered on task-specific autonomic response, even when ultra-short time series are considered. [ABSTRACT FROM AUTHOR]

In the present article, we investigated a delay-based eco-epidemic prey–predator system in the presence of environmental fluctuations where predators engage with susceptible and infected prey, adopting Holling type II and ratio-dependent functional responses, respectively. During the study of the considered model, we identify each potential equilibrium point and its local stability criterion. The basic reproduction number has been computed, and the backward bifurcation about the disease-free equilibrium point was analyzed. The article illustrates Hopf bifurcation, global stability at the endemic equilibrium point, and their graphical depiction. We look over the variations in the dynamics of non-delay, delayed, and stochastic systems, revealing that a fixed level of temporal delay results in chaotic motion for the increasing strength of the saturation constant yet is potentially controlled by the predator growth rate. To study the dynamic behavior of the solution of the considered system and verify all theoretical results, we use numerical simulation and minutely analyze the influence of model parameters on the solution of the considered system. The stochastic transition is studied by varying the strength of stochastic fluctuation and the effect of delay. [ABSTRACT FROM AUTHOR]

A free-electron laser is a laser that has the same optical properties as a conventional laser, such as emitting beams of coherent electromagnetic radiation, which can reach high powers, but uses some very different principles of operation to form the beams. The chaotic motion of electrons causes a considerable decrease in the gain and efficiency of free-electron lasers. In this paper, the Hamiltonian of the dual-wiggler free-electron laser with and without axial guide magnetic field is constructed. Hamilton's equations of motion were derived exactly for both cases. The steady-state solution is also derived and investigated so that the initial conditions of the system are clear. The Poincaré surface-of-section maps were plotted after solving Hamilton's equations of motion numerically, where the chaotic behavior of the system was obvious when the axial field was included while the motion became regular and the Hamiltonian is integrable in the absence of the axial guide magnetic field. Regular orbits are observed clearly for large values of the axial field. [ABSTRACT FROM AUTHOR]

This narrative review, the second of 2 parts about a new approach to the diagnosis and treatment of psychiatric disorders that is based on dynamical systems theory, describes the implications of evidence for the practical applicability of this theory and its quantitative tools. Importance: Dynamical systems theory is widely used to explain tipping points, cycles, and chaos in complex systems ranging from the climate to ecosystems. It has been suggested that the same theory may be used to explain the nature and dynamics of psychiatric disorders, which may come and go with symptoms changing over a lifetime. Here we review evidence for the practical applicability of this theory and its quantitative tools in psychiatry. Observations: Emerging results suggest that time series of mood and behavior may be used to monitor the resilience of patients using the same generic dynamical indicators that are now employed globally to monitor the risks of collapse of complex systems, such as tropical rainforest and tipping elements of the climate system. Other dynamical systems tools used in ecology and climate science open ways to infer personalized webs of causality for patients that may be used to identify targets for intervention. Meanwhile, experiences in ecological restoration help make sense of the occasional long-term success of short interventions. Conclusions and Relevance: Those observations, while promising, evoke follow-up questions on how best to collect dynamic data, infer informative timescales, construct mechanistic models, and measure the effect of interventions on resilience. Done well, monitoring resilience to inform well-timed interventions may be integrated into approaches that give patients an active role in the lifelong challenge of managing their resilience and knowing when to seek professional help. [ABSTRACT FROM AUTHOR]

This narrative review describes a new approach to the diagnosis and treatment of psychiatric disorders that is based on dynamical systems theory, which addresses the concepts of tipping points, cycles, and chaos in complex systems. Importance: Psychiatric disorders may come and go with symptoms changing over a lifetime. This suggests the need for a paradigm shift in diagnosis and treatment. Here we present a fresh look inspired by dynamical systems theory. This theory is used widely to explain tipping points, cycles, and chaos in complex systems ranging from the climate to ecosystems. Observations: In the dynamical systems view, we propose the healthy state has a basin of attraction representing its resilience, while disorders are alternative attractors in which the system can become trapped. Rather than an immutable trait, resilience in this approach is a dynamical property. Recent work has demonstrated the universality of generic dynamical indicators of resilience that are now employed globally to monitor the risks of collapse of complex systems, such as tropical rainforests and tipping elements of the climate system. Other dynamical systems tools are used in ecology and climate science to infer causality from time series. Moreover, experiences in ecological restoration confirm the theoretical prediction that under some conditions, short interventions may invoke long-term success when they flip the system into an alternative basin of attraction. All this implies practical applications for psychiatry, as are discussed in part 2 of this article. Conclusions and Relevance: Work in the field of dynamical systems points to novel ways of inferring causality and quantifying resilience from time series. Those approaches have now been tried and tested in a range of complex systems. The same tools may help monitoring and managing resilience of the healthy state as well as psychiatric disorders. [ABSTRACT FROM AUTHOR]

Purpose: Pair formation is an important step in pair trading that has only been examined manually or through numerical instructions. These methods fail in the multivariate mode and do not consider conflicting goals in the problem structure. In this research, a method is presented to create multivariate pair combinations by considering contradictory multiple goals in stock pair trading. Methodology: In this study, the statistical sample is limited to the top 30 companies listed on the Tehran Stock Exchange due to the need for high-frequency transactions. The problem is developed in the form of a Mixed Integer Programming (MIP) model, and due to non-convex constraints and exponential solution space, a multi-objective genetic algorithm is used to obtain multivariate pair combinations. To achieve multiple goals, the developed type of genetic algorithm, namely, The Chaotic Non-dominated Sorting Genetic Algorithm (CNSGA-II), was used. In this method, chaos theory is used to create the initial population of the genetic algorithm in order to obtain appropriate and high-precision solutions. Findings: The results showed that the use of chaos theory could increase the degree of convergence in evolutionary algorithms. In addition, these results indicate the superiority of the multi-objective pair trading strategy based on the distance approach over the traditional single-objective model. Originality/Value: In order to optimize pair trading, the Non-dominated Sorting Genetic Algorithm was used. Also, the initial population of individuals was created in a multi-objective genetic algorithm based on chaos theory. [ABSTRACT FROM AUTHOR]

Chaos theory offers a unique lens to understand the intricate relationships between economic growth and energy supply pricing. Existing economic theories often emphasize energy prices' inherent randomness, unpredictability, and economic growth. A deeper comprehension can be achieved by applying chaos theory to this complex system. Developing a dynamic model that captures the causal relationships among the various variables impacting economic growth, energy supply, and pricing is crucial for unraveling this complexity. This study aims to delve into the chaotic nature of the energy economy system within the context of economic growth. The research methodology is rooted in a fundamental-applied approach. By employing numerical simulation techniques, specifically utilizing the Simulink MATLAB toolbox, the study seeks to explore and potentially control chaos within the system. The findings highlight the system's nonlinear dynamics, showcasing its sensitivity to initial conditions and exhibiting chaotic behavior, limit cycles, and stable equilibrium points across varying initial values. This research endeavor contributes to a more nuanced understanding of the interplay between energy economics, economic growth, and pricing dynamics. [ABSTRACT FROM AUTHOR]

The interaction of different time scales in predator-prey models has become a common research topic. In the present article, we concentrated on the dynamics of interactions at two time scales in a plankton-fish system. To investigate the effects of the two time scales on plankton-fish dynamics, we constructed a new parameter with a corrected type that differs from the traditional slow parameter. In addition, zooplankton's refuge from the predator and phytoplankton mortality due to competition are incorporated into the model. Positivity and boundedness of solutions were proved. We then discussed feasibility and stability conditions of the equilibrium. We used a variety of means to support the existence of chaos in the system. Hopf bifurcation conditions were also obtained. Chaos control in the plankton-fish model is one of the main motivations for this study. In the slow-variable parameter case, we explored the control mechanism of gestation delay on chaotic systems, which are calmed by different periodic solutions. Moreover, under seasonal mechanisms, external driving forces can stabilize the system from chaos to periodic oscillations. Meanwhile, the sliding mode control (SMC) approach quickly calms chaotic oscillations and stabilizes it to an internal equilibrium state. The necessary numerical simulation experiments support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the possibilities of complex nonlinear dynamic signal generation using a simple photorefractive two-wave mixing system without any feedback using numerical simulations. The novel idea is to apply a sinusoidal electric field to the system inroder to extract nonlinear dynamic behavior. The mathematical model of the system was constructed using Kogelnick's coupled wave equations and Kukhtarev's material equation. The spatio-temporal evolution of the system was simulated in discrete steps numerically. The temporal evolution of the output light intensity exhibits period doubling, behavior which is a characteristic feature of complex nonlinear dynamic systems. A bifurcation diagram and Lyapunov exponentials confirm the presence of the period-doubling route to chaos in the system. The observed complex signal pattern varies uniformly with respect to the amplitude of the applied field, indicating a controllable nonlinear dynamic behavior. Such a system can be very useful in applications such as photonic reservoir computing, in-materio computing, photonic neuromorphic networks, complex signal detection, and time series prediction. [ABSTRACT FROM AUTHOR]

The disassembly of spent lithium batteries is a prerequisite for efficient product recycling, the first link in remanufacturing, and its operational form has gradually changed from traditional manual disassembly to robot-assisted human–robot cooperative disassembly. Robots exhibit robust load-bearing capacity and perform stable repetitive tasks, while humans possess subjective experiences and tacit knowledge. It makes the disassembly activity more adaptable and ergonomic. However, existing human–robot collaborative disassembly studies have neglected to account for time-varying human conditions, such as safety, cognitive behavior, workload, and human pose shifts. Firstly, in order to overcome the limitations of existing research, we propose a model for balancing human–robot collaborative disassembly lines that take into consideration the load factor related to human involvement. This entails the development of a multi-objective mathematical model aimed at minimizing both the cycle time of the disassembly line and its associated costs while also aiming to reduce the integrated smoothing exponent. Secondly, we propose a modified multi-objective fruit fly optimization algorithm. The proposed algorithm combines chaos theory and the global cooperation mechanism to improve the performance of the algorithm. We add Gaussian mutation and crowding distance to efficiently solve the discrete optimization problem. Finally, we demonstrate the effectiveness and sensitivity of the improved multi-objective fruit fly optimization algorithm by solving and analyzing an example of Mercedes battery pack disassembly. [ABSTRACT FROM AUTHOR]

Heart monitoring improves life quality. Electrocardiograms (ECGs or EKGs) detect heart irregularities. Machine learning algorithms can create a few ECG diagnosis processing methods. The first method uses raw ECG and time-series data. The second method classifies the ECG by patient experience. The third technique translates ECG impulses into Q waves, R waves and S waves (QRS) features using richer information. Because ECG signals vary naturally between humans and activities, we will combine the three feature selection methods to improve classification accuracy and diagnosis. Classifications using all three approaches have not been examined till now. Several researchers found that Machine Learning (ML) techniques can improve ECG classification. This study will compare popular machine learning techniques to evaluate ECG features. Four algorithms--Support Vector Machine (SVM), Decision Tree, Naive Bayes, and Neural Network--compare categorization results. SVM plus prior knowledge has the highest accuracy (99%) of the four ML methods. QRS characteristics failed to identify signals without chaos theory. With 99.8% classification accuracy, the Decision Tree technique outperformed all previous experiments. [ABSTRACT FROM AUTHOR]

Fractional-order (FO) chaotic systems exhibit richer and more complex dynamic behaviors compared to integer-order ones. This inherent richness and complexity enhance the security of FO chaotic systems against various attacks in image cryptosystems. In the present study, a comprehensive examination of the dynamical characteristics of the fractional-order Arneodo (FOAR) system with cubic nonlinearity is conducted. This investigation involves the analysis of phase planes, bifurcation diagrams, Lyapunov exponential spectra, and spectral entropy. Numerical studies show that the Arneodo chaotic system exhibits chaotic behavior when the lowest fractional-order (FO) value is set to 0.55. In this context, the aim is to securely encrypt biomedical images based on the Arneodo chaotic system with the lowest FO value using the Nvidia Jetson Nano development board. However, though the lowest FO system offers enhanced security in biomedical image encryption due to its richer dynamic behaviors, it necessitates careful consideration of the trade-off between high memory requirements and increasing complexity in encryption algorithms. Within the scope of the study, a novel random number generator (RNG) is designed using the FOAR chaotic system. The randomness of the random numbers is proven by using internationally accepted NIST 800-22 and ENT test suites. A biomedical image encryption application is developed using pseudo-random numbers. The images obtained as a result of the application are evaluated with tests such as histogram, correlation, differential attack, and entropy analyses. As a result of the study, it has been shown that encryption and decryption of biomedical images can be successfully performed on a mobile Nvidia Jetson Nano development card in a secure and fast manner. [ABSTRACT FROM AUTHOR]

Background: This research delves into the complexity management of collaborative networks and interorganizational systems in the health innovation ecosystem on the basis of a best practice in the coronavirus disease 2019 (COVID-19) crisis. The objective is to offer specific solutions and guidelines to stakeholders in the health innovation ecosystem to control the chaos resulting from unexpected events along the ecosystem development and evolution path. Methods: For this purpose, the performance of the Health Innovation Ecosystem in Iran (the Every Home is a Health Base plan) has been examined through a detailed and in-depth analysis of events and actions taken using documents, reports and interviews with experts. The practical application of chaos and complex adaptive system features (adaptation, time horizons, edge of chaos, sensitivity to initial conditions, state space and strange attractors) is introduced to identify and manage the transition from a state where the health innovation ecosystem is on the edge of chaos and prone to failure. Data were collected through studying documents, reports and interviews with experts, and then analysed using qualitative content analysis techniques, open and axial coding and metaphors derived from complexity and chaos theories. Results: The findings indicate that to understand and embrace the complexity of the health innovation ecosystem throughout its development and evolution and manage and lead it through the edge of chaos towards successful interorganizational systems performance, it is necessary to use gap analysis to achieve consensus, establish a highly interactive governance structure with key stakeholders of the ecosystem, maintain flexibility to control bifurcations (butterfly effect), prevent transforming emergency solutions into standard routines and ensure the sustainability of the ecosystem against future threats by long-term financial security. Conclusions: This research provides insights into the dynamics of complex health systems and offers strategies for promoting successful innovation through collaborative networks and interorganizational systems in the development and evolution of the health innovation ecosystem. By embracing complexity and chaos, healthcare professionals, policy-makers and researchers can collaboratively address complex challenges and improve outcomes in health network activities. The conclusion section provides guidelines for successfully managing the complexity of the ecosystem and offers suggestions for further research. [ABSTRACT FROM AUTHOR]

Nowadays, establishing security in data transmission is essential, and it is achieved by cryptography. Encryption of still or video images in specific applications such as Internet of Things, medical and satellite imaging, in applications requiring high-speed encryption, or even in applications where a personal computer is unavailable or cannot be used needs special hardware. In this paper, an image encryption algorithm based on chaos theory named Parallel Chaotic Checksum-based Image Encryption or PCCIE algorithm is proposed that has been able to provide a fast, efficient and secure algorithm with a hardware perspective on the design and parallel system structure. Using high-level synthesis, PCCIE is implemented on a Field Programmable Gate Array (FPGA). The proposed algorithm using small and independent local image buffers solved FPGA internal memory limitation for encryption of large images. Ultimately, a Hexa-core crypto-processor with single-precision floating-point and fixed-point precision has been designed, capable of encrypting 256 × 256 and Full HD images in 2.13 and 59.52 milliseconds, respectively, at 469 and 16 frames per second. [ABSTRACT FROM AUTHOR]

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields. [ABSTRACT FROM AUTHOR]

In order to solve the dynamic analysis and chaotic motion control problems of the current-mode-controlled Boost converter system, a state equation model in the continuous current mode is established. The evolutionary path of the periodic motion of the system through the doubling bifurcation to the chaotic motion is analyzed by the bifurcation diagram, Poincaré sections and phase portraits. Then, according to the fundamental principle of the resonant parametric perturbation (RPP) method, a controller is designed based on the model-free adaptive control (MFAC) method to output the perturbation amplitude, and the disturbance quantity is calculated according to the perturbation amplitude. By adding a small amplitude disturbance to the controllable parameter of the controlled system, the chaotic motion of the system is guided to expected periodic orbit. The advantage of this method is that no precise mathematical model (PMM) of the system is required. At the same time, the design of the controller is simple and easy to implement. [ABSTRACT FROM AUTHOR]

This article is a tribute to Oleksandr Mykolayovych Sharkovsky, a renowned mathematician and one of the founders of the mathematical concept of deterministic chaos. Sharkovsky's groundbreaking work, including his famous Sharkovsky theorem, has had a significant impact on the theory of dynamical systems. The article highlights Sharkovsky's early life, education, and career, as well as his contributions to the field of mathematics. It also mentions his achievements, such as publishing 10 monographs and over 250 research works, and receiving several prestigious awards. Sharkovsky's work continues to be influential in the study of nonlinear dynamics and chaos theory. [Extracted from the article]

Smartphones, digital cameras, and other imaging devices generate vast amounts of high-resolution colored images daily, stored on devices equipped with multi-core central processing units or on the cloud. Safeguarding these images from potential attackers has become a pressing concern. This paper introduces a set of six innovative image ciphers designed to be stronger, faster, and more efficient. Three of these algorithms incorporate the State-Based Tent Map (SBTM) Chaotic Pseudo Random Number Generator (CPRNG), while the remaining three employ a proposed modified variant, SBTMPi. The Grayscale Image Cipher (GIC), Colored Image Cipher Single-Thread RGB (CIC1), and Colored Image Cipher Three-Thread RGB (CIC3) showcase the application of the proposed algorithms. By incorporating novel techniques in the confusion and diffusion phases, these ciphers demonstrate remarkable performance, particularly with large colored images. The study underscores the potential of SBTM-based image ciphers, contributing to the advancement of secure image encryption techniques with robust random number generation capabilities. [ABSTRACT FROM AUTHOR]

The security and integrity of medical data, in particular, have become significant concerns due to the substantial expansion in the healthcare environment due to the internet of things (IoT). To guarantee data security during transmission, this research suggests a chaotic healthcare monitoring system. This system employs a new 5- dimension (5D) chaotic system in conjunction with the secure hash algorithm version three (SHA3-256), salsa 20, and deoxyribonucleic acid (DNA). Lyapunov's proposed 5D chaos system was tested and passed for several initial periods, yielding a super chaos system (3 positive Lyapunov). Salsa 20 and randomly generated chaotic keys were utilized for encryption and decryption operations. The method we created will assess a patient's body temperature, heart rate, and oxygen saturation levels in the blood and communicate the data to a healthcare center through the Message Queuing Telemetry Transport (MQTT) protocol. The suggested system ensures that patient data is transmitted via the internet or an intranet in a secure, reliable, and readily accessible manner. In several studies involving security analysis, The encryption time is 1.872, the throughput (in bits per second (bps)) is 273.2642, and the memory usage (in megabytes) is 10.6211. The performance analysis confirmed the proposed cryptosystem's capacity to withstand multiple attacks due to its low computational and communication costs and broad key space. [ABSTRACT FROM AUTHOR]

Due to the potential security problem of the key management and distribution for the symmetric image encryption schemes, this paper proposes a new asymmetric image encryption method based on a singular cubic curve and chaos theory. The Diffie-Hellman algorithm is used to generate the initial values of a chaotic map by exchanging public keys. The image encryption process is carried out using a chaotic map, in which a random sequence of the same length as the image to be encrypted is generated using the standard map, and then bitwise XOR is used to create confusion in the image's pixels. Also, an Arnold cat map is used to change the location of pixels and diffusion in them is obtained. Gray images with size 256×256 are used in this algorithm. The simulation results and security analysis indicate that the scheme can withstand common attacks such as statistical attacks, differential attacks, and other attacks. [ABSTRACT FROM AUTHOR]

The short-term traffic flow prediction can help to reduce flight delays and optimize resource allocation. Using chaos dynamics theory to analyze the chaotic characteristics of en-route traffic flow is the basis of short-term en-route traffic flow prediction and ensuring the orderly and smooth state of the en-route. This paper takes the time series of en-route traffic flow extracted from Automatic-Dependent Surveillance Broadcast (ADS-B) measured data as the research object, uses the improved C–C method to reconstruct the phase space, and uses the improved small data volume method to calculate the Lyapunov index to identify the chaos phenomenon of en-route traffic flow. In order to avoid the interference of chaos phenomenon on traffic prediction, the Wavelet Neural Network (WNN) model is established to predict the traffic flow at en-route points. The experimental shows that when the number of iterations is 10,000, the average accuracy of WNN prediction is 0.87173, and the average running time is 6.9335334 s. According to the experimental results, it can be seen that the smaller number of iterations has more advantages in running time, which greatly reduces the overall running time. At the same time, it indicates that appropriately increasing or reducing the number of iterations in this experiment has little effect on the results. [ABSTRACT FROM AUTHOR]

Memristors have several chaotic dynamic models and have been used successfully in various fields, including secure communication systems, information storage, and artificial neural networks. The memristor-based four-dimensional chaotic (FDMC) systems generate unpredictable and intricate time domain signals. Parameter fluctuations in the FDMC system may give birth to chaos, making it difficult to suppress. Stabilizing chaos in the FDMC system improves the circuit's performance. This paper synthesizes a novel time-efficient chatter-free nonlinear robust adaptive control (NLRAC) technique that stabilizes chaos in the FDMC system affected by time-varying unknown bounded exogenous disturbances and model uncertainties. The proposed NLRAC strategy decimates the time-varying unknown bounded exogenous disturbances and model uncertainties effects; it establishes a faster, smoother state-variable trajectories convergence to the zero vicinity. The theoretical analysis and mathematical proofs are based on the Lyapunov stability technique. Computer simulation results show that the proposed NLRAC technique effectively brings the FDMC system's state-variable trajectories to zero with reduced fluctuations for control input signals and state-variable trajectories. This feedback controller's attribute enhances closed-loop stability performance, improves precision, and reduces risk overshoot. The paper includes comparative computer simulation results to endorse the proposed controller performance. [ABSTRACT FROM AUTHOR]

Nonlinear dynamical problems, characterized by unpredictable and chaotic changes among variables over time, pose unique challenges in understanding. This paper explores the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation-a fundamental equation in applied magnetism and nanophysics. The study focuses on dynamic behaviors, specifically examining bifurcations and equilibrium points leading to chaotic phenomena by introducing an external term to the system. Employing chaos theory, we showcase the chaotic tendencies of the perturbed dynamical system. Additionally, a sensitivity analysis using the Runge-Kutta method reveals the solution's stability under slight variations in initial conditions. Innovatively, the paper utilizes the planar dynamical system technique to construct various solitons within the governing model. This research provides novel insights into the behavior of the (2+1)-dimensional cmKdV equation and its applications in applied magnetism and nanophysics. [ABSTRACT FROM AUTHOR]

The present paper provides a historical context for chaos theory, originating in the 1960s with Edward Norton Lorenz's efforts to predict weather patterns. It introduces chaos theory, fractal geometry, nonlinear dynamics, and the butterfly effect, highlighting their exploration of complex systems. The authors aim to bridge the gap between chaos theory and oral and maxillofacial surgery (OMFS) through a literature review, exploring its applications and emphasizing the prevention of minor deviations in OMFS to avoid significant consequences. A comprehensive literature review was conducted on PubMed, Web of Science, and Google Scholar databases. The selection process adhered to the PRISMA-ScR guidelines and Leiden Manifesto principles. Articles focusing on chaos theory principles in health sciences, published in the last two decades, were included. The review encompassed 37 articles after screening 386 works. It revealed applications in outcome variation, surgical planning, simulations, decision-making, and emerging technologies. Potential applications include predicting infections, malignancies, dental fractures, and improving decision-making through disease prediction systems. Emerging technologies, despite criticisms, indicate advancements in AI integration, contributing to enhanced diagnostic accuracy and personalized treatment strategies. Chaos theory, a distinct scientific framework, holds potential to revolutionize OMFS. Its integration with advanced techniques promises personalized, less traumatic surgeries and improved patient care. The interdisciplinary synergy of chaos theory and emerging technologies presents a future in which OMFS practices become more efficient, less traumatic, and achieve a level of precision never seen before. [ABSTRACT FROM AUTHOR]

DC microgrids have emerged as a promising solution to provide reliable and efficient power for various applications. However, similar to any power system, DC microgrids are prone to faults that can disrupt their performance. Accordingly, the lack of publication of sufficient standards and guidelines for the protection of DC microgrids makes it necessary to develop protection methods in these networks. Therefore, the purpose of this paper is to create a new fault detection method in islanded DC microgrids. In this method, the current signal samples are entered into a chaotic state, and using the feature of sensitivity to the initial conditions of this method, it accurately identifies the fault. In this case, the signal undergoes a very large chang during the fault, which is easily visible compared to the normal state. It should be noted that, unlike other methods, in the proposed method in this paper, only one measurement unit is used in the DC bus for sampling signals. Therefore, there is no need to use communication links in the proposed method. The proposed method has been implemented using MATLAB/Simulink software on a sample DC microgrid. The results show that the proposed method is capable to detect pole-to-pole and pole-to-ground faults on the microgrids and also faults on the distributed generations and electrical vehicles. Also, results prove that this method is resistant to the operational uncertainty of distributed generations, electrical vehicles, and the destructive effects of noise on the sampled signals. [ABSTRACT FROM AUTHOR]

This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have established the occurrence of various types of bifurcations, including flip bifurcation and Neimark-Sacker bifurcation. Furthermore, to address the observed chaotic behavior in the system, three controllers were designed by employing state feedback control, OGY feedback control, and hybrid control methods. These controllers serve to control chaos in the proposed system and identify specific conditions under which chaos or bifurcations can be stabilized. Finally, the theoretical analyses have been validated through numerical simulations. [ABSTRACT FROM AUTHOR]

This study draws on the parallelism between digitalization and the complexity of the Islamic banking industry (IBs) in a postpandemic era. It examines the digital Butterfly Effect on the Islamic banking industry to promote tech-driven IBs through an empirical lens. The study constructs a Fintech adoption index (FADi) and uses a Bayesian vector Auto-Regressive model, causality tests and impulse response functions for yearly data from 2008 to 2022 to examine the possible magnified effect of adopting Fintech by the Islamic banking industry in Malaysia. Key findings suggest that embracing Fintech by the IBs enhances the profitability of the banks, which is measured by the return on asset and return on equity. In addition, the study reports a ripple effect of FADi on the broader spectrum of the Malaysian economy. This indicates that Fintech fosters economic growth, household consumption, financial and insurance services, and corporate taxes. On the other hand, Fintech adoption helps reduce the unemployment rate. The findings contribute to the literature by investigating the IB as a system within financial chaos theory and the possible Butterfly Effect triggered by Fintech adoption. [ABSTRACT FROM AUTHOR]

Metaheuristic techniques are capable of representing optimization frames with their specific theories as well as objective functions owing to their being adjustable and effective in various applications. Through the optimization of deep learning models, metaheuristic algorithms inspired by nature, imitating the behavior of living and non-living beings, have been used for about four decades to solve challenging, complex, and chaotic problems. These algorithms can be categorized as evolution-based, swarm-based, nature-based, human-based, hybrid, or chaos-based. Chaos theory, as a useful approach to understanding neural network optimization, has the basic idea of viewing the neural network optimization as a dynamical system in which the equation schemes are utilized from the space pertaining to learnable parameters, namely optimization trajectory, to itself, which enables the description of the evolution of the system by understanding the training behavior, which is to say the number of iterations over time. The examination of the recent studies reveals the importance of chaos theory, which is sensitive to initial conditions with randomness and dynamical properties that are principally emerging on the complex multimodal landscape. Chaotic optimization, in this regard, accelerates the speed of the algorithm while also enhancing the variety of movement patterns. The significance of hybrid algorithms developed through their applications in different domains concerning real-world phenomena and well-known benchmark problems in the literature is also evident. Metaheuristic optimization algorithms have also been applied to deep learning or deep neural networks (DNNs), a branch of machine learning. In this respect, the basic features of deep learning and DNNs and the extensive use of metaheuristic algorithms are overviewed and explained. Accordingly, the current review aims at providing new insights into the studies that deal with metaheuristic algorithms, hybrid-based metaheuristics, chaos-based metaheuristics as well as deep learning besides presenting recent information on the development of the essence of this branch of science with emerging opportunities, applicability-based optimization aspects and generation of well-informed decisions. [ABSTRACT FROM AUTHOR]

We explore the transition to chaos in a prototypical hydrodynamic oscillator, namely a globally unstable low-density jet subjected to external time-periodic forcing. As the forcing strengthens at an off-resonant frequency, we find that the jet exhibits a sequence of nonlinear states: period-1 limit cycle $\rightarrow $ quasiperiodicity $\rightarrow$ intermittency $\rightarrow$ low-dimensional chaos. We show that the intermittency obeys type-II Pomeau–Manneville dynamics by analysing the first return map and the scaling properties of the quasiperiodic lifetimes between successive chaotic epochs. By providing experimental evidence of the type-II intermittency route to chaos in a globally unstable jet, this study reinforces the idea that strange attractors emerge via universal mechanisms in open self-excited flows, facilitating the development of instability control strategies based on chaos theory. [ABSTRACT FROM AUTHOR]

To research the special transmission system type of the multistage closed-loop gear system of the 3D braiding machine, a multi-degree of freedom nonlinear dynamic model was established by using the lumped mass method, taking into account parameters such as meshing stiffness, static transmission error, backlash, and meshing damping. To reduce the computational complexity, a gear system with 12 gears was selected and solved using the Runge-Kutta method. Using meshing frequency, backlash, and meshing damping ratio as control parameters, we analyzed the bifurcation and chaos of the system under different conditions through bifurcation diagrams. Simultaneously using sequence diagram, phase plane diagrams, Poincare maps, and FFT diagrams to accurately display the motion state of the system. The analysis results indicate that with the increase of meshing frequency and backlash, the system exhibits a range of motion states, such as period-one motion, multi-periodic motion, quasi-periodic motion, and chaotic motion. Meanwhile, increasing the damping ratio can effectively suppress the chaotic state of the gear system and also reduce the maximum vibration displacement of the gear system. [ABSTRACT FROM AUTHOR]