Search

We review the recent results of large ensemble climate projections considering them to be the simulations of chaotic systems. The quick spread of an initially localized ensemble in the first weeks after initialization is an appearance of the butterfly effect, illustrating the unpredictability of the dynamics. We show that the growth rate of uncertainty (an analog of the Lyapunov exponent) can be determined right after initialization. The next phase corresponds to a convergence of the no longer localized ensemble to the time-dependent climate attractor and requires a much longer time. After convergence takes place, the ensemble faithfully represents the climate dynamics. Concerning a credible simulation, the observed signal should then wander within the spread of the converged ensemble all the time, i.e., to behave just as any of the ensemble members. As a manifestation of the chaotic-like climate dynamics, one can imagine that beyond the single, observed time-dependent climate, a plethora of parallel climate realizations exists. Converged climate ensembles also define the probability distribution by which the physical quantities of the different climate realizations occur. Large ensemble simulations were shown earlier to be credible in the sense formulated. Here, in addition, an extended credibility condition is given, which requires the ensemble to be a converged ensemble, valid also for low-dimensional models. Interestingly, to the best of our knowledge, no low-order physical or engineering systems subjected to time-dependent forcings are known for which a comparison between simulation and experiment would be available. As illustrative examples, the CESM1-LE climate model and a chaotic pendulum are taken. [ABSTRACT FROM AUTHOR]

In this paper, based on a three-dimensional Bao system, a memristor-based hyper-chaotic Bao-like system is successfully constructed, and a simulated equivalent circuit is designed, which is used to verify the chaotic behaviors of the system. Meanwhile, a control method called periodically intermittent control with variable control width is proposed. The control width sequence in the proposed method is not only variable, but also monotonically decreasing, and the method can effectively stabilize most existing nonlinear systems. Moreover, the memristor-based hyper-chaotic Bao-like system is controlled by combining the proposed method with the Lyapunov stability principle. Finally, we should that the proposed method can effectively control and stabilize not only the proposed hyper-chaotic system, but also the Chua's oscillator. [ABSTRACT FROM AUTHOR]

Comprehension of the structure of software will facilitate maintaining the software more efficiently. Clustering software modules, as a reverse engineering technique, is assumed to be an effective technique in extracting comprehensible structural-models of software from the source code. Finding the best clustering model of a software system is regarded as a NP-complete problem. Minimizing the connections among the created clusters, maximizing the internal connections within the created clusters and maximizing the clustering quality are considered to be the most important objectives in software module clustering (SMC). Poor success rate, low stability and modularization quality are regarded as the major drawbacks of the previously proposed methods. In this paper, five different heuristic algorithms (Bat, Cuckoo, Teaching–Learning-Based, Black Widow and Grasshopper algorithms) are proposed for optimal clustering of software modules. Also, the effects of chaos theory in the performance of these algorithms in this problem have been experimentally investigated. The results of conducted experiments on the eight standard and real-world applications indicate that performance of the BWO, PSO, and TLB algorithms are higher than the other algorithms in SMC problem; also, the performance of these algorithm increased when their initial population were generated with logistic chaos method instead of random method. The average MQ of the generated clusters for the selected benchmark set by BWO, PSO and TLB are 3.155, 3.120 and 2.778, respectively. [ABSTRACT FROM AUTHOR]

The possibilities of micrometeorological resilience in urban contexts immersed in a basin geographical configuration are investigated. For this purpose, time series data with measurements of meteorological variables (temperature, magnitude of wind speed and relative humidity) and atmospheric pollutants (PM2.5, PM10, CO) are analyzed through chaos theory, calculating the coefficient of Lyapunov (λ), the correlation dimension (Dc), the Hurst coefficient (H), the correlation entropy (SK), the fractal dimension (D) and the Lempel–Ziv complexity (LZ). Indicators are built for each measurement period (2010–2013 and 2017–2020), for each locality studied and located at different heights. These indicators, which correspond to the quotient between the entropy resulting from the meteorological variables and that of the pollutants, show sensitivity to height. Another important indicator, for identical measurement conditions, arises from the calculation of the fractal dimensions of the meteorological variables and that of the pollutants, which allows for comparative studies between the two periods. These indicators are conclusive in pointing out that, in a large city with basin geographical characteristics, subjected to an intensive urbanization process, there is no micrometeorological resilience and a great variation occurs in the initial conditions. [ABSTRACT FROM AUTHOR]

Economic disequilibrium theory (DT) more realistically represents modern macroeconomic systems than general equilibrium theory. DT coupled with applied mathematical economics and nonlinear dynamical analysis generates multi-dimensional phase spaces. Interdependencies of endogenous variables in state space create a flow of different and "parallel economic realities," which depend on the initial conditions. By modeling variable changes using the nonlinear least squares (NLLS) method, we define the first-order nonlinear ordinary differential equation (NODE) system. The NODE system is impossible to solve analytically. The numerical solution and visualization requires the MATLAB software package, combined with its specialized applications pplane (two-dimensional (2D)) and MATCONT (three-dimensional (3D)). By analyzing the evolution of flow operators, we can predict the future qualitative behavior of the entire system, determine the model-optimal values, and perform inverse modeling for variables. The obtained data advocate better and more stable macroeconomic paths that economic policymakers can pursue. The proposed methodology's boundaries have strong links to chaos theory. Chaotic behavior can arise after a certain number of periods. We found very high computation accuracy, transformation of discrete variables to continuous functions, and the implementation of high-order polynomial data fitting offset its effects in part and to some reasonable degree. [ABSTRACT FROM AUTHOR]

In this paper, we come up with three secure chaos-based stream ciphers, implemented on an FPGA board, for data confidentiality and integrity. To do so, first, we performed the statistical security and hardware metrics of certain discrete chaotic map models, such as the Logistic, Skew-Tent, PWLCM, 3D-Chebyshev map, and 32-bit LFSR, which are the main components of the proposed chaotic generators. Based on the performance analysis collected from the discrete chaotic maps, we then designed, implemented, and analyzed the performance of three proposed robust pseudo-random number generators of chaotic sequences (PRNGs-CS) and their corresponding stream ciphers. The proposed PRNGs-CS are based on the predefined coupling matrix M. The latter achieves a weak mixing of the chaotic maps and a chaotic multiplexing technique or XOR operator for the output function. Therefore, the randomness of the sequences generated is expanded as well as their lengths, and divide-and-conquer attacks on chaotic systems are avoided. In addition, the proposed PRNGs-CS contain polynomial mappings of at least degree 2 or 3 to make algebraic attacks very difficult. Various experimental results obtained and analysis of performance in opposition to different kinds of numerical and cryptographic attacks determine the high level of security and good hardware metrics achieved by the proposed chaos system. The proposed system outperformed the state-of-the-art works in terms of high-security level and a high throughput which can be considered an alternative to the standard methods. [ABSTRACT FROM AUTHOR]

Considering that chaotic systems are immersed in multiple areas of science and nature and that their dynamics are governed by a great sensitivity to the initial conditions and variations in their parameters, it is of great interest for the scientific community to have tools to characterize and reproduce these trajectories. Two dynamic chaotic systems whose equations are based on the jerky system are used as benchmarks, i.e., the Memristive Shaking Chaotic System (MSCS) and the Unstable Dissipative System of type I (UDSI). One characteristic common to them is their simple mathematical structure and the complexity of their solutions. Therefore, this paper presents a strategy for identifying chaotic trajectories using a recurrent wavelet first-order neural network (RWFONN) that is trained online with an error filtering algorithm and considering the Morlet-wavelet as an activation function. The parameters of the network are adjusted considering the Euclidean distance between the solutions. Finally, the results depict proper identification of the chaotic systems studied through analysis and numerical simulation to validate the behavior and functionality of the proposed network. [ABSTRACT FROM AUTHOR]

For some transmission shafting, nonlinear supports are connected to beam structures through the pattern of the contact surface. Nonlinear foundations are typically installed to the beam structure for a limited range. The unsuitable installation mode of nonlinear foundations will make the parameters of nonlinear foundations no longer uniform. Most existing studies ignore the boundary rotational restraints of beam structures and concentrated mass introduced by the nonlinear supports or foundations. To improve the engineering acceptance of beam structures with nonlinearity, it is of great significance to study the dynamic behavior of the generally restrained pre-pressure beam structure with a partial non-uniform foundation of nonlinear stiffness. This study establishes the nonlinear vibration model of the beam structure with a local non-uniform nonlinear stiffness distribution. Nonlinear dynamic responses of the beam structure are predicted by the Galerkin truncation method (GTM). Mode functions of the generally restrained pre-pressure beam structure are set as the trail and weight function. The correctness of the GTM for dynamic prediction of the beam structure with a partial non-uniform nonlinear foundation is verified by using the harmonic balance method (HBM). The influence of sweeping ways of excitations and parameters of the partial non-uniform nonlinear foundation on nonlinear dynamic responses of the beam structure are investigated. Dynamic responses of the beam structure with a partial non-uniform nonlinear foundation are sensitive to their initial values. Vibration states of the beam structure are transformed effectively by changing parameters of the partial non-uniform nonlinear foundation. The vibration at both ends of the beam structure can be suppressed by applying suitable parameters of the partial non-uniform nonlinear foundation. [ABSTRACT FROM AUTHOR]

In this paper, the main subharmonic resonance of the Mathieu–Duffing system with a quintic oscillator under simple harmonic excitation, the route to chaos, and the bifurcation of the system under the influence of different parameters is studied. The amplitude-frequency and phase-frequency response equations of the main resonance of the system are determined by the harmonic balance method. The amplitude-frequency and phase-frequency response equations of the steady solution to the system under the combined action of parametric excitation and forced excitation are obtained by using the average method, and the stability conditions of the steady solution are obtained based on Lyapunov's first method. The necessary conditions for heteroclinic orbit cross section intersection and chaos of the system are given by the Melnikov method. Based on the separation of fast and slow variables, the bifurcation phenomena of the system under different conditions are obtained. The amplitude-frequency characteristics of the total response of the system under different excitation frequencies are investigated by analytical and numerical methods, respectively, which shows that the two methods achieve consistency in the trend. The influence of fractional order and fractional derivative term coefficient on the amplitude-frequency response of the main resonance of the system is analyzed. The effects of nonlinear stiffness coefficient, parametric excitation term coefficient, and fractional order on the amplitude-frequency response of subharmonic resonance are discussed. Through analysis, it is found that the existence of parametric excitation will cause the subharmonic resonance of the Mathieu–Duffing oscillator to jump. Finally, the subcritical and supercritical fork bifurcations of the system caused by different parameter changes are studied. Through analysis, it is known that the parametric excitation coefficient causes subcritical fork bifurcations and fractional order causes supercritical fork bifurcations. [ABSTRACT FROM AUTHOR]

Investigation of the dynamical behavior related to environmental phenomena has received much attention across a variety of scientific domains. One such phenomenon is global warming. The main causes of global warming, which has detrimental effects on our ecosystem, are mainly excess greenhouse gases and temperature. Looking at the significance of this climatic event, in this study, we have connected the ACT-like model to three climatic components, namely, permafrost thaw, temperature, and greenhouse gases in the form of a Caputo fractional differential equation, and analyzed their dynamics. The theoretical aspects, such as the existence and uniqueness of the obtained solution, are examined. We have derived two different sliding mode controllers to control chaos in this fractional-order system. The influences of these controllers are analyzed in the presence of uncertainties and external disturbances. In this process, we have obtained a new controlled system of equations without and with uncertainties and external disturbances. Global stability of these new systems is also established. All the aspects are examined for commensurate and non-commensurate fractional-order derivatives. To establish that the system is chaotic, we have taken the assistance of the Lyapunov exponent and the bifurcation diagram with respect to the fractional derivative. To perform numerical simulation, we have identified certain values of the parameters where the system exhibits chaotic behavior. Then, the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic coupled map lattices with nonlinear perturbations (NPDCML) is proposed. The test results show that the new spatiotemporal chaotic system has more obvious advantages than CML system in spatiotemporal performance and chaotic characteristics, and NPDCML system has larger parameter space and better cryptographic characteristics. Based on NPDCML system, a new image encryption scheme is proposed, which adopts the method of diffusion before confusion. After a round of diffusion, the image is scrambled by decomposing the bit plane, and the image is further encrypted by the way of mutual diffusion of high bit plane and low bit plane. Through the analysis of various test results, the encryption scheme can resist most common attacks, and it is proved that NPDCML system has good chaotic characteristics and cryptographic advantages. [ABSTRACT FROM AUTHOR]

The Šeba billiard, a rectangular torus with a point scatterer, is a popular model to study the transition between integrability and chaos in quantum systems. Whereas such billiards are classically essentially integrable, they may display features such as quantum ergodicity [ 11 ], which are usually associated with quantum systems whose classical dynamics is chaotic. Šeba proposed that the eigenfunctions of toral point scatterers should also satisfy Berry's random wave conjecture, which implies that the value distribution of the eigenfunctions ought to be Gaussian. However, Keating, Marklof, and Winn formulated a conjecture that suggested that Šeba billiards with irrational aspect ratio violate the random wave conjecture, and we show that this is indeed the case. More precisely, for tori having diophantine aspect ratio, we construct a subsequence of the set of new eigenfunctions having even/even symmetry, of essentially full density, and show that its 4th moment is not consistent with a Gaussian value distribution. In fact, given any set |$\Lambda $| interlacing with the set of unperturbed eigenvalues, we show non-Gaussian value distribution of the Green's functions |$G_{\lambda }$|⁠ , for |$\lambda $| in an essentially full density subsequence of |$\Lambda $|⁠. [ABSTRACT FROM AUTHOR]

Background: The socio-environmental aspects of southern Assam reflect a general pattern of backwardness. Moreover, child healthcare resources in the region are inadequately used, leading to low vaccination coverage. Given this background, this paper attempted to comprehend wealth-based inequality in full vaccination in rural areas of southern Assam. Methodology: Based on a multistage cluster sampling approach, 360 children of 12–23 months were selected from the study area. To identify the predictors of a child, a non-linear model was estimated by using the generalized linear model (GLM) approach followed by Erreygers decomposition technique to quantify the wealth inequality in the obtained predictors in explaining the disparity in full vaccination. Result: The Bacillus Calmette–Guérin (BCG) vaccination recorded the highest vaccination coverage, at nearly 90% and the lowest was observed for the measles vaccine, around 61 percent. Slightly more than half of the eligible children (54 percent) were vaccinated against all the Universal Immunization Programme (UIP)-recommended vaccines. The decomposition analysis revealed that the occupation of the child's father, maternal age, birth order of the child, and health-seeking behavior such as antenatal care (ANC) were the prime factors related to inequality in full vaccination in the region. Conclusion: Vaccination coverage in the region has improved over time, however, full vaccination is concentrated towards the economically advantaged section of the society in rural southern Assam. Targeted, context-specific, and expanded government initiatives could aid in addressing the overall wealth-related full vaccination inequalities in the valley. [ABSTRACT FROM AUTHOR]

This study discusses the existence of a significant deficit in the various institutions of the international system dealing with the spread and multiplicity of international crises. To deal with them from the angle of symptoms and results and not look for the causes and roots of these problems. The study adopted the network analysis approach by examining the idea of globalization itself and the logic on which it is based, which facilitated the outbreak and spread of crises. The study concluded that the fragility and weakness of the governance of the international system resulting from the chaos of the international system, and the absence of an international authority over states that control and regulate the behavior of states increased the spread of crises. Moreover, it led to the complexity of managing relations between the main actors in the international system and challenging opportunities to build new rules and standards that regulate relations between them. [ABSTRACT FROM AUTHOR]

Fractional order maps are a hot research topic; many new mathematical models are suitable for developing new applications in different areas of science and engineering. In this paper, a new class of a 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The hyperchaotic map has no equilibrium and lines of equilibrium points, depending on the values of the system parameters. All of the chaotic attractors generated by the proposed fractional map are hidden. The system dynamics are analyzed via bifurcation diagrams, Lyapunov exponents, and phase portraits for different values of the fractional order. The results show that the fractional map has rich dynamical behavior, including hidden homogeneous multistability and offset boosting. The paper also illustrates a novel theorem, which assures that two hyperchaotic fractional discrete systems achieve synchronized dynamics using very simple linear control laws. Finally, the chaotic dynamics of the proposed system are stabilized at the origin via a suitable controller. [ABSTRACT FROM AUTHOR]

This article is based on my own experience of listening to the music of Adam Michna while reading a book by James Gleick about chaos theory. Chaos theory covers a range of approaches - to medicine, weather forecasting, geometry - that challenge intuitive understandings of how the universe works. For me, the music and the ideas seemed to "fuse" in a way which was extremely powerful, but also resistant to traditional modes of analysis. When we add to this mix the elusive effect of Czechness, and the actual difficulty of recouping just what happened in the past, the stakes go up immeasurably. In the end I argue that we must rigorously ask ourselves what we know and how we think we know it, and acknowledge that documents and documentation alone will tell us almost nothing of real value. Part of the responsibility of our field involves the investigation of uncertainties. [ABSTRACT FROM AUTHOR]

Rivaroxaban is a popular direct factor Xa inhibitor used for anticoagulation therapy in patients with nonvalvular atrial fibrillation (NVAF). The aim of this study was to establish a population pharmacokinetic (PPK) model for rivaroxaban in elderly Chinese patients with nonvalvular atrial fibrillation, evaluate precision dosing regimens, and analyze hemorrhagic risk after rivaroxaban treatment. A 1‐compartment population PK model with estimated glomerular filtration rate (eGFR), total bilirubin (TBIL), and ABCB1 rs1045642 as major covariates for apparent clearance was developed using the nonlinear mixed‐effects model (NONMEM). A Monte Carlo simulation was performed to evaluate various dosing schemes and different levels of covariates for the target range of therapeutic drug‐monitoring concentrations (Cmax,ss and Cmin,ss). The exposure to rivaroxaban was simulated and assessed through hemorrhagic risk evaluation. The results showed that the average probability of target attainment (PTA) for optimal dosing regimens with different covariate levels for the targeted Cmax,ss and Cmin,ss were 29.35% to 31.3% and 64.91% to 65.8%, respectively. A dosage of 10 mg of rivaroxaban in elderly Chinese patients with normal renal and liver function was appropriate. The area under the concentration–time curve estimated over 24 hours with precision dosing at steady state (AUC24,ss) was statistically significantly associated with an increased risk of bleeding events (OR 1.0006, 95%CI 1.0003 to 1.001, P <.0001), and the bleeding risk increased by 1.82‐fold for every 1000 μg*h/L increase in AUC24,ss. A lower dose is recommended for elderly patients with renal impairment to avoid overexposure and bleeding events. The PPK model could inform individualized dosing for elderly Chinese patients with nonvalvular atrial fibrillation receiving rivaroxaban anticoagulation therapy. [ABSTRACT FROM AUTHOR]

The coexistence of different attractors with fixed parameters affords versatility in the performance of the dynamical system. As a result, recent research has focused on defining nonlinear oscillators with infinite coexisting attractors, the vast majority of which are non-autonomous systems. In this study, we present an infinite number of equilibriums achieved with the simplest autonomous megastable oscillator. To begin, we explore the symmetry property of distinct coexisting attractors, such as periodic, quasi-periodic, and chaotic attractors. The dynamical properties of the proposed system are further investigated using phase portraits, Lyapunov exponents spectrum, and bifurcation diagram using the local maxima of the state variables. The detailed investigation reveals that the proposed system has a wide range of dynamical properties ranging from periodic oscillations to hyperchaos. Linear quadratic regulator (LQR) control-based controllers are designed to control the chaos in the proposed system and also achieve synchronization between proposed systems that have different initial conditions. The effectiveness of the controller designed based on LQR is presented by simulation results. It is shown that the proposed system converges asymptotically to the desired equilibrium point, and the synchronization between the slave and the master systems is achieved by converging the error to zero after controllers are activated. [ABSTRACT FROM AUTHOR]

An intellectual journey that began with the discovery of strange attractors derived from Chua's circuit, their translation into physical shapes by means of 3D printers, and finally, to the production of jewelry is presented. After giving the mathematical characteristics of Chua's circuit, we explain the chaotic design process, used for creating jewels, providing specifications of the used methodological approach, for its reproduction. We discuss the feasibility of this approach and the transmission of scientific contents on chaos theory, usually restricted to university students, in a high school Science, Technology, Engineering, Art, and Mathematics course, for the realization of advanced educational processes, implemented both in computational and real environments. We think that the idea of transforming science into art forms can drive students in acquiring scientific knowledge and skills, allowing them to discover the inner beauty of chaos. [ABSTRACT FROM AUTHOR]

Higher education faces dramatic transformations in demographics, politics, culture, labor, and technology—all of which are compounded by the COVID-19 pandemic. Chaos theory offers perspectives for weathering these changes, though ultimately, as the future remains unpredictable, the best instructors can offer is doing their best in their jobs. [ABSTRACT FROM AUTHOR]

This paper presents new directions in the modeling of electric arc furnaces. This work is devoted to an overview of new approaches based on random differential equations, artificial neural networks, chaos theory, and fractional calculus. The foundation of proposed solutions consists of an instantaneous power balance equation related to the electric arc phenomenon. The emphasis is mostly placed on the conclusions that come from a novel interpretation of the equation coefficients. [ABSTRACT FROM AUTHOR]

Rotary kiln temperature forecasting plays a significant part of the automatic control of the sintering process. However, accurate forecasts are difficult owing to the complex nonlinear characteristics of rotary kiln temperature time series. With the development of chaos theory, the prediction accuracy is improved by analyzing the essential characteristics of time series. However, the existing prediction methods of chaotic time series cannot fully consider the local and global characteristics of time series at the same time. Therefore, in this study, the global recurrence plot (GRP)-based generative adversarial network (GAN) and the long short-term memory (LSTM) combination method, named GRP-lstmGAN, are proposed, which can effectively display important information about time scales. First, the data is subjected to a series of pre-processing operations, including data smoothing. Then, transforming one-dimensional time series into two-dimensional images by GRP makes full use of the global and local information of time series. Finally, the combination of LSTM and improves GAN models for temperature time series prediction. The experimental results show that our model is better than comparison models. [ABSTRACT FROM AUTHOR]

A hydraulic generator regulating system with electrical, mechanical, and hydraulic constitution is a complex nonlinear system, which is analyzed in this research. In the present study, the dynamical behavior of this system is investigated. Afterward, the input/output feedback linearization theory is exerted to derive the controllable model of the system. Then, the chaotic behavior of the system is controlled using a robust controller that uses a Chebyshev neural network as a disturbance observer in combination with a non-singular robust terminal sliding mode control method. Moreover, the convergence of the system response to the desired output in the presence of uncertainty and unexpected disturbances is demonstrated through the Lyapunov stability theorem. Finally, the effectiveness and appropriate performance of the proposed control scheme in terms of robustness against uncertainty and unexpected disturbances are demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

In this work, we studied the complex behaviors of the fractional-order financial chaotic system, consisting of a simple, relatively chaotic system with two quadratic nonlinearities (QN) and a sextic nonlinearity (SN). We completed and enriched the results presented in the study of Subartini et al. (2021). As a result of this, our study focused more on the fractional order and adaptive finite-time sliding mode control in the financial risk chaotic system. The dynamical behaviors of the financial chaotic system (FCS) with two QN and an SN were analyzed, and the stability was investigated via the Cardano method. The stability analysis showed that the real part of all the roots was negative, which confirmed the stability of the new system under the typical parameters. By using the MATLAB simulation, these properties were characterized, including the phase portraits, 0-1 test, Poincaré map, bifurcation diagram, and Lyapunov exponent. The analysis showed that the financial risk chaotic system of fractional order was able to exhibit chaotic behavior and periodical behavior. In spite of external perturbations and uncertainty, an adaptive finite-time sliding mode control strategy was devised to guide the states of the financial chaotic system to the origin in a finite amount of time. MATLAB phase plots were employed in this study to illustrate all the main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamical behavior of a one-dimensional piecewise map based on the logistic map, where generalized multistability can be observed. The proposed system has the unique property that the function is symmetric with respect to the origin but not its behavior, furthermore this system can display three types of multistability, and chaos for both, monostable and bistable behaviors. The stability analysis of the proposed system is presented. We describe the structure of bistable regions in the bifurcation diagram. Particular attention is paid to the chaotic regions. Corresponding to coexisting attractors, three scenarios of coexisting attractors, namely fixed points, periodic orbits, and chaotic attractors, can be found, which are unreported behaviors in discrete chaotic systems. The mechanism that leads to multistability phenomenon including pitchfork bifurcation, period-halving bifurcations, and the coexisting invariant sets is demonstrated. Furthermore, the Lyapunov exponent is analyzed with the type of multistability distinguished for a given set of parameters. [ABSTRACT FROM AUTHOR]

Dynamics of chemical reactor systems are found with highly nonlinear behavior. Computational modeling of a fractional-order chemical reactor system and investigating nonlinear dynamical changes and its control are the main focus of this research work. Chaos theory is a blooming fertile field in recent years, which is used widely to quantify nonlinear behaviors such as quasi-oscillations, bi-stability and bifurcation. The work starts from deriving state-space model of the system with first-order differential equations. There are six equilibrium points and the Jacobian matrix is derived for investigating the stability of the equilibrium points. Eigenvalues of each equilibrium point are calculated. Based on the sign of the real part of the eigenvalues and the existence of imaginary part, we found two equilibrium points behave as saddle spirals and the remaining four equilibrium points are saddle nodes. The stability of the system for different parameter values is investigated and presented. The influence of parameters in the system dynamics is discussed and significant parameter values are highlighted for further study. We considered Caputo's definition for formulating the fractional-order (FO) model of the system based on the advantages highlighted in various literatures. The stable and unstable regions are portrayed with parameter variations. The results clarified that the analysis can be refined using fractional-order treatment of chaotic systems. We proceeded with our investigation towards obtaining different oscillations, particularly chaotic oscillations. The challenges lie in finding the proper fractional order to handle the system. We showed the bifurcation diagram for a range of fractional-order values and clarified the transitions from periodic oscillations to chaotic behavior and period-doubling bifurcations. The phase portraits are presented to show the limit cycle oscillations for fractional-order 0.95, period-doubling during 0.98, and chaotic oscillations for higher values. We proceeded with our investigation with fractional-order as 0.99. Bifurcation plots for parameter variation are obtained. Chaotic regions, periodic oscillations, period-halving and period-doubling are observed and the influences are discussed. We emphasize the intricate properties which are not addressed during the integer-order treatment of the system and nail the importance of fractional-order treatment. An adaptive sliding mode (ASM) controller is derived and implemented to control the system precisely. The effectiveness is shown by providing simulation results of the system with parameter estimation and controlled state time history plots. The work can be extended to verify the simulated results with equivalent electronic circuits. [ABSTRACT FROM AUTHOR]

With the regular development of the global epidemic, the global port shipping supply is tight. The problem of port congestion, soaring freight rates, and hard-to-find container space has emerged. This paper proposes a new joint berth-quay crane allocation model, namely E-B&QC, by taking the minimum of the time in the port of the ship, the cost of extra transportation distance for collector trucks in the land area of the port, and the cost of extra waiting time for ships. Then, the deficiencies of the sparrow search algorithm (SSA) are considered in solving the E-B&QC model, and the SSA is improved based on the three-dimensional Cat chaos mapping and quantum computing theory. Chaotic Quantum Sparrow Search Algorithm (CQSSA) is proposed, population individual coding rules are formulated, also E-B&QC model solving algorithm is established. Finally, a new berth-crane allocation optimization method, namely, E-B&QC-CQSSA, is proposed. Subsequently, the feasibility and superiority of the proposed allocation model and solution algorithm are tested according to the actual data of a small river port in the south and a medium-sized river port in the north. Simulation examples show that the E-B&QC model can develop different high-quality solutions for container ports under different working conditions, and the more complex the actual situation of the port, the more significant the optimization effect. The proposed CQSSA for E-B&QC model can obtain a better solution. [ABSTRACT FROM AUTHOR]

Experts and researchers in the field of information security have placed a high value on the security of image data in the last few years. They have presented several image encryption techniques that are more secure. To increase the security level of image encryption algorithms, this article offers an efficient diffusion approach for image encryption methods based on onedimensional Logistic, three-dimensional Lorenz, DNA encoding and computing, and SHA-256. The encryption test demonstrates that the method has great security and reliability. This article, also, examines the security of encryption methods, such as secret key space analysis, key sensitivity test, histogram analysis, information entropy process, correlation examination, and differential attack. When the image encryption method described in this article is compared to several previous image encryption techniques, the encryption algorithm has higher information entropy and a lower correlation coefficient. [ABSTRACT FROM AUTHOR]

Observability analysis of a bioinspired flexible flapping wing system provides a measure of how well the states of flexible flapping wing micro-aerial vehicles can be estimated from real-time measurements during high-speed flight. However, the traditional observability analysis approaches have trouble in terms of lack of quantitative analysis index, high computational complexity, low accuracy, and unavailability in stochastic systems with memory, including bioinspired flexible flapping wing systems. Therefore, a novel derivative-free observability analysis method is proposed here based on the generalized polynomial chaos expansion. By formulating a surrogate model to represent the relationship between the cumulative measurement and the random initial state, the observability coefficient matrix is calculated and the observability rank condition is stated. Consequently, several observability indices are proposed to quantity the observability of the system. Altogether, the proposed method avoids the disadvantages of the traditional approaches, especially in assessing the observability degree of each state and the effect of stochastic noise on observability. The validation of the proposed method is first provided by demonstrating the equivalence between the traditional and proposed methods and subsequently by comparing the observability of the Lorenz system calculated via three different approaches. Finally, the proposed method is applied on a bioinspired flexible wing system to optimize the placement of sensors, which is consistent with the natural configuration of campaniform sensilla on the wing of the hawkmoth. [ABSTRACT FROM AUTHOR]

To safeguard private information, image steganography is extensively used. Research is focused on ways to enhance steganographic technologies so that they may increase compression ratio while maintaining steganography image integrity. Because of its essential qualities such as security, scalability, and robustness, Steganography is a preferred way of communicating protected secret information to prevent hacking and misuse. This proposed research offers a steganography approach based on Enhanced Chaotic Particle Swarm Optimization (ECPSO), which uses chaos theory to determine the optimal pixel positions in the cover picture to hide confidential information when keeping the steganography quality in the images. Both the cover and secret pictures are separated into blocks to increase hiding capacity, with each component storing a sufficient quantity of secret data by mapping the pixels. The suggested ECPSO-Stegano system has better results with the criteria of Mean Square Error (MSE) of 0.00018%, Peak-Signal-to-Noise-Ratio (PSNR) of 79.66%, Bit Error Rate (BER) of 0.45% in average, and Structural Similarity Index (SSI) of 0.98 in average for various input size. It's also robust to statistical threats. [ABSTRACT FROM AUTHOR]

Internet of things (IoT) provides several applications such as intelligent urban transportation, smart factory, and smart health. In such systems, the transmitted data are important and must be secured to prevent destructive and unauthorized access to critical data. Indeed, existing IoT solutions come with conventional cryptographic techniques such as AES, RSA, and DES. However, some of these algorithms are no longer reliable and others require significant resources in terms of energy, memory, and computing power, making them unsuitable for IoT nodes that may have limited resources. To address these challenges, this paper develops a new lightweight and efficient cryptosystem to secure IoT communications. The proposed cryptosystem is composed of a chaos-based random generator, confusion, and diffusion blocks. Through a use case, the experimental results, at implementation and statistical levels, demonstrate good performances. The implementation results in the Mbed microcontroller NXP LPC1768 include low memory usage, fast encryption and decryption speed, and low energy consumption. The statistical results confirm the robustness of the proposed cryptosystem against many attacks according to the NIST test, key size, key sensitivity, information entropy, and statistical histogram analysis. Compared to related works, this paper proposes an enhanced lightweight cryptosystem with optimized confusion–diffusion layers that can be implemented in different resource-constrained hardware boards. Moreover, the proposed solution does not make any assumptions about the data types to be used in IoT networks. It is open to any type (sensing value, text, voice, image, etc.). These features guarantee the potential use of the proposed cryptosystem in many real-world applications. [ABSTRACT FROM AUTHOR]

In the current circumstance, the Web Service Composition (WSC) was introduced to address complex user needs concerning the Quality of Services (QoS). In the WSC problem, the user needs are divided into a set of tasks. The corresponding web services are retrieved from the web services discovery according to the functionality of each task, and have different non-functional constraints, such as QoS. The WSC problem is a multi-objective optimization problem and is classified as an NP-hard problem. The whale optimization algorithm (WOA) is proven to solve complex multi-objective optimization problems, and it has the advantage of easy implementation with few control parameters. In this work, we contribute to improving the WOA algorithm, where different strategies are introduced to enhance its performance and address its shortcomings, namely its slow convergence speed, which produces low solution accuracy for the WSC problem. The proposed algorithm is named Improved Whale Optimization Algorithm (IWOA) and has three different strategies to enhance the performance of the WOA. Firstly, the Sine chaos theory is proposed to initiate the WOA's population and enhance the initialization diversity. Secondly, a Lévy flight mechanism is proposed to enhance the exploitation and exploration of WOA by maintaining the whales' diversity. Further, a neighborhood search mechanism is introduced to address the trade-off between exploration and exploitation searching mechanisms. Different experiments are conducted with datasets on 12 different scales (small, medium, and large), and the proposed algorithm is compared with standard WOA and five state-of-the-art swarm-based algorithms on 30 different independent runs. Furthermore, four evaluation criteria are used to validate the comparison: the average fitness value, best fitness values, standard deviation, and average execution time. The results show that the IWOA enhanced the WOA algorithm's performance, where it got the better average and best fitness values with a low variation on all datasets. However, it ranked second regarding average execution time after the WOA, and sometimes third after the WOA and OABC, which is reasonable because of the proposed strategies. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which is based on Lyapunov stability theory. To verify synchronization is achieved between the systems, we performed the numerical simulation. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of bursting, mixed-mode oscillations (MMOs) and horseshoe chaos in a mixed Rayleigh–Liénard oscillator with asymmetric double well potential driven by parametric periodic damping and external excitations. The dynamical behaviours of the considered model, when the exciting frequency is much smaller than the natural frequency, are studied using bifurcation diagrams, Lyapunov exponent diagrams, time histories and phase portraits. It is found that our model displays various bursting and mixed-mode oscillations. Moreover, various mixed-mode oscillation routes to chaos occur in the system. It is also found that the system exhibits two or three coexisting behaviours of attractors when the parametric damping coefficient evolves. On the other hand, the analytical criterion for the appearance of horseshoes chaos is derived using the Melnikov method. A convenient demonstration of the accuracy of the method is obtained from the fractal basin boundary. It is noted that the increase of the impure quadratic damping coefficient, cubic damping coefficient, asymmetric term and the amplitude of the external excitation accentuates the chaotic behaviour of the system. However, the behaviour of the system becomes regular as the parametric damping coefficient increases. [ABSTRACT FROM AUTHOR]

In this research, the ship power system is studied with a fractional-order approach. A 2-D model of a two-generator parallel-connected is considered. A chaotic attractor is observed for particular parameter values. The fractional-order form is calculated with the Adam–Bashforth–Moulton method. The chaotic response is identified even for the order 0.99. Phase portrait is generated using the Caputo derivative approach. Wolf's algorithm is used to calculate Lyapunov exponents. For the considered values of parameters, one positive Lyapunov exponent confirms the existence of chaos. Bifurcation diagrams are presented to analyze the various dynamical behaviors and bifurcation points. Interestingly, the considered system is multistable. Also, antimonotonicity, period-doubling, and period halving are observed in the bifurcation diagram. As the last step, a fractional-order controller is designed to remove chaotic dynamics. Time plots are simulated to show the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

There has been a great deal of interest in researching the behavior of chaotic systems over the past decade. They are distinguished by their sensitivity to initial conditions, continuous broad-band power spectrum, and similarity to random behavior. Chaos has possible applications in the encryption, compression, and modulation blocks of a digital communication system. The possibility of self-synchronization of chaotic oscillations has spawned a deluge of research on the cryptographic applications of chaos. FAC (Factoring) and CM (Chaotic maps) are used in this research to develop a new signature system (CM). Our system has a higher security level than any other based on a single hard number-theoretic problem since it is extremely unlikely that FAC and CM can be solved effectively at the same time. We further demonstrate that the scheme's performance involves only minimal operations in signing and validating logarithms, and that it is impervious to attack. [ABSTRACT FROM AUTHOR]

A mobile ad hoc network (MANETs) is a collection of moving nodes that combine into a network with no predefined infrastructure. There are many types of attacks that could target MANETS, one among them is Distributed Denial of service attacks (DDoS). DDoS is defined as attacking routing functions and taking down the entire operation of the mobile ad hoc network. The two primary victims of DDoS attacks are the functions of routing and battery capacity. The DDoS attack can cause routing table overflow which in turn can potentially cause the infected node floods. The routing overflow is followed by creating a fake route packet to consume the available resources of the participating active nodes. This cause disrupts the normal functioning of legitimate routes. In recent years, different approaches are implemented to improve the security level of MANET. In this work, the Cuckoo Search Algorithm-based Modified Elman's Neural Network (CSA - MENN) approaches have been proposed to overcome DDoS attacks. The CSA - MENN approaches consists of three-part which are Cuckoo search algorithm clustering area to enhance the route from source to destination, chaos theory module is used to detect the abnormal nodes, then the Modified Elman Neural Network (MENN) is employed to prevent a malicious node from sending data to the destination by determining node that consumed more resources. Packets could be lost or the victim could reset the path between the attacker and itself. CICIDS dataset has been used to test and evaluate the performance of the proposed approach based on the criteria of accuracy, packet loss, and jitter. The data set, CICIDS 2017, used in this article divides the data into 7 groups: 5 for training, 1 for validation, and 1 for generalization. In summary, approximately 71.4 percent of data is used for training and 28.6 percent for validation and generalization. [ABSTRACT FROM AUTHOR]

The microcontroller implementation, controls, and synchronization of a three-dimensional (3D) autonomous system with a parabolic equilibrium point are investigated in this paper. The system in question displays a reverse period doubling route hidden chaotic attractors with two different shapes. Then, the partial and total amplitude controls of the system are achieved by inserting two parameters. A microcontroller implementation is performed in order to confirm the results obtained from the numerical simulations. It is found that the results from the numerical simulations and microcontroller implementation qualitatively agree with each other. The sliding mode controllers are designed to control chaos in the system under study. With the sliding mode control method, the numerical simulations confirm that chaos can be controlled in the 3D autonomous system with a parabolic equilibrium point. In addition, two chaotic 3D autonomous systems with a parabolic equilibrium point and the same parameters are synchronized by the use of a unidirectional linear error feedback coupling scheme. Finally, an active control technique is applied to bring about chaos synchronization between two chaotic 3D autonomous systems with a parabolic equilibrium and different parameters. [ABSTRACT FROM AUTHOR]

A new chaotic system is obtained by changing the number of unknown parameters. The dynamical behavior of the chaotic system is investigated by the exponential change of the single unknown parameter and the state variable in the nonlinear term of the system. The structure of the newly constructed chaotic system is explored. When the number of the same state variables in the nonlinear term of the chaotic system varies, the system's dynamic behavior undergoes complex changes. Moreover, with the exponential change of a single-state variable in a three-dimensional system, the system maintains the chaotic attractor while the state of the attractor changes. On this basis, the Lyapunov exponent, bifurcation diagram, complexity, and 0–1 test are used to compare and analyze this phenomenon. Through circuit simulations, the chaotic characteristics of the system under different conditions are further verified; this provides a theoretical basis for the hardware implementation of the new system. Finally, the new chaotic system is applied to an image encryption system with the same encryption and decryption processes. The comparison shows improved encryption and decryption characteristics of image encryption systems. [ABSTRACT FROM AUTHOR]

In this paper, based on sliding-mode control, a finite-time adaptive synchronization method is introduced to realize the generalized projective synchronization of fractional-order memristor chaotic systems with unknown parameters. First, a class of memristor chaotic system is extended to fractional order, and the chaos characteristics of the system are studied. Then a new fractional-order integral sliding-mode surface with faster convergence speed is designed, which can make the error system converge to zero in finite time. Next the controller with adjustable parameters and the adaptive laws are designed, and the sufficient condition for the sliding-mode surface can be reached by the synchronization error system in finite time and the unknown parameters can be identified in finite time is obtained. Finally, the numerical simulations show that the generalized projection synchronization and unknown parameter identification of fractional-order memristor chaotic system can be realized in a short time under the proposed synchronization strategy. [ABSTRACT FROM AUTHOR]

This paper devotes to the qualitative geometric analysis of the traveling wave solutions of MEW‐Burgers wave equation. Firstly, MEW‐Burgers equation is transformed into an equivalent planar dynamical system by using traveling wave transformation. Then the global structure of the planar system is presented, and solitary waves, kink waves (anti‐kink waves), and periodic waves are found. Secondly, Jacobi stability for the planar system is studied based on KCC theory, and Jacobi stability of any point on the trajectory of system is dicussed. The dynamical behavior of the deviation vector near the equilibrium points is analyzed, and the numerical simulation is consistent with the theoretical analysis. Lyapunov stability and Jacobi stability of the equilibrium points are also compared and analyzed. The obtaining results show that Lyapunov stability of the equilibrium points of the system is not exactly consistent with Jacobi stability. Finally, the planar system with periodic disturbance is transformed into a six dimensional nonlinear system, and the periodic, quasi‐periodic, and chaotic dynamical behaviors of the system are numerically simulated. [ABSTRACT FROM AUTHOR]

The feed forward neural network (FNN) has a significant breakthrough in recent times in solving different real-life complex problems. The success of FNN is primarily attributed to its architecture, the optimization technique used, and the tuning of hyper-parameters to identify different patterns in data. This study tries to find an optimization technique that will play a vital role in an FNN to get better results. Whale optimization algorithm (WOA) is one of the popular nature-inspired optimization techniques used to solve real-time sciences and engineering problems. A new optimization approach namely chaotic oppositional-based whale optimization algorithm (COWOA) is developed in this paper, for the first time, to discuss the FNN problems of four different dataset by integrating chaotic function and oppositional-based learning with WOA. Simulation results are presented to validate the success of the suggested COWOA approach and demonstrate its dominance over basic WOA, chaotic WOA (CWOA), particle swarm optimization (PSO), Adam optimization algorithm (AOA), and stochastic gradient descent (SGD) for both unimodal and multimodal dataset problems. The comparative analysis with other optimization techniques validates its superiority and robustness on four standard dataset of FNN problem. Furthermore, to validate the performance of the proposed algorithm, a statistical analysis is performed. The outcome of the statistical results validates the superiority and acceptability of COWOA over other optimization methods. [ABSTRACT FROM AUTHOR]

Microgrid (MG) systems are growing at a rapid pace since they can accommodate the high amount of renewable energy. Since the MG consists of small distributed generators (DG) with volatile characteristics, an efficient energy management system is the main requisite in MG. In this paper, a chaotic sine cosine algorithm with crossover operator (CSCAC) is proposed for the day-ahead MG optimal energy scheduling problem. CSCAC includes a novel non-linear transition parameter based on the chaos system which can help the algorithm escape from local optima. A chaotic search operator is proposed to enhance the local search ability. Furthermore, a crossover operator is devised to combine the advantages of different search strategies and achieve a comparatively better balance of exploration and exploitation. First, the effectiveness of CSCAC is validated on several benchmark functions. Then, it is applied to the day-ahead energy scheduling in a MG with three wind power plants, two photovoltaic power plants and a combined heat and power plant (CHP). Furthermore, it is implemented in two more cases considering the uncertainty and stochastic nature of the renewable power sources. Experimental results demonstrate the superiority of CSCAC over other comparative algorithms in the optimal MG energy management problem. [ABSTRACT FROM AUTHOR]

Infidelity is a challenging but prominent issue in couple therapy. In addition to the negative outcomes, clinicians generally report that infidelity is the second most difficult problem to treat after intimate partner violence. The purpose of this study was to identify the recovery process in the betrayed (non-participating) partner. Specifically, we sought to identify the implications of online infidelity (infidelity that occurs through Internet modalities, such as social media messaging, direct messages, etc.) on the betrayed partner during recovery. Across three focus groups of those in dating relationships, we identified an eight-stage process through the lens of the betrayed partner: intuition, investigation, discovery, confrontation, response, forgiveness/limbo, termination, and new rules. Theoretical and clinical implications are discussed. [ABSTRACT FROM AUTHOR]

Numerous field data and experiments on the perching birds or songbirds show that the fear of predators can cause significant changes in the prey population. Fear of predatory populations increases the chances of survival of the prey population, and this can greatly reduce the reproduction of the prey population. The influence of fear has contributed a leading role in both the environmental biology and theoretical ecology. Taking into account the interaction of predator–prey with non-overlapping generations, a discrete-time model is proposed and studied. Keeping in mind the biological feasibility of species, the existence of fixed points is studied along with the local asymptotic behavior of the proposed model around these fixed points. Furthermore, taking into account the oscillatory behavior of the model, various types of bifurcations are analyzed about biologically feasible fixed points with an application of center manifold theory and bifurcation theory of normal forms. Existence of chaos is discussed, and fluctuating and chaotic behavior of the system is controlled through implementation of different chaos control procedures. The illustration of theoretical discussion is carried out via validation of observed experimental field data and appropriate numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, a new 4D chaos system is introduced based on the mathematical structure through composing and transferring. The behavior of the proposed chaotic system is studied using different tests, such as Lyapunov exponent, bifurcation diagram and histogram. In order to show the advantage of the new chaos system, the proposed system is used for image encryption. In the proposed algorithm, in addition to the new chaos system, cellular automata is also used to improve the security of the algorithm. The proposed algorithm has a separate structure for encryption key, which increases the security of the proposed algorithm. The security of the proposed environment which is evaluated using different types of security tests shows the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]