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Provided are three program listings which may be used to illustrate this fractal figure. Extensions of these algorithms and their use in the study of chaos and fractals are suggested. (CW)

Offers several LOGO programs to study the behavior of simple nonlinear systems. Suggests that LOGO is an excellent tool for studying chaotic systems. Offers suggestions for different forms of LOGO. Builds upon programs presented in a previous article. (MVL)

In this paper, we investigate a discrete-time prey-predator model. The model is formulated by using the piecewise constant argument method for differential equations and taking into account Holling type III. The existence and local behavior of equilibria are studied. We established that the system experienced both Neimark-Sacker and perioddoubling bifurcations analytically by using bifurcation theory and the center manifold theorem. In order to control chaos and bifurcations, the state feedback method is implemented. Numerical simulations are also provided for the theoretical discussion. [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]

Adaptive network models arise when describing processes in a wide range of fields and are characterized by some specific effects. One of them is mixed dynamics, which is the third type of chaos in addition to the conservative and dissipative types. In this work, we consider a more complex type of connections between network elements—simplex, or higher-order adaptive interactions. Using numerical simulation methods, we analyze various characteristics of mixed dynamics and compare them with the case of pairwise couplings. We found that mixed dynamics in the case of simplex interactions is characterized by a very high similarity of a chaotic attractor to a chaotic repeller, as well as a stronger closeness of the sum of the Lyapunov exponents of the attractor and repeller to zero. This means that in the case of three elements, the conservative properties of the system are more pronounced than in the case of two. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a nonlinear discrete prey-predator system with fear effects. The existence, local stability and boundedness of positive equilibrium point are discussed. Using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation in the interior of R²+ are established. Furthermore, the numerical simulations not only show complex dynamical behaviors, but also verify our analysis results. A feedback control strategy is employed to control bifurcation and chaos in the system. [ABSTRACT FROM AUTHOR]

Recent studies demonstrate that the reproduction of prey is suppressed by the fear of predators. However, it will not respond immediately to fear, but rather reduce after a time lag. We propose a diffusive predator-prey model incorporating fear response delay into prey reproduction. Detailed bifurcation analysis reveals that there are three different cases for the effect of the fear response delay on the system: it might have no effect, both stabilizing and destabilizing effect, or destabilizing effect on the stability of the positive equilibrium, respectively, which are found by numerical simulations to correspond to low, intermediate or high level of fear. For the second case, through ordering the critical values of Hopf bifurcation, we prove the existence of stability switches for the system. Double Hopf bifurcation analysis is carried out to better understand how the fear level and delay jointly affect the system dynamics. Using the normal form method and center manifold theory, we derive the normal form of double Hopf bifurcation, and obtain bifurcation sets around double Hopf bifurcation points, from which all the dynamical behaviors can be explored, including periodic solutions, quasi-periodic solutions and even chaotic phenomenon. [ABSTRACT FROM AUTHOR]

An analytical classification in a three-dimensional parameter space is presented to describe the dynamics for an extended Lorenz system of the Li-Ou type, conditions are given to find supercritical and degenerate Hopf bifurcations and a pitchfork bifurcation. Finally, the theoretical results are compared with numerical simulations and bifurcation diagrams. [ABSTRACT FROM AUTHOR]

This study examines discrete-time T system. We begin by listing the topological divisions of the system's fixed points. Then, we analytically demonstrate that a discrete T system sits at the foundation of a Neimark Sacker(NS) bifurcation under specific parametric circumstances. With the use of the explicit Flip-NS bifurcation criterion, we establish the flip-NS bifurcation's reality. Center manifold theory is then used to establish the direction of both bifurcations. We do numerical simulations to validate our theoretical findings. Additionally, we employ the 0-1 test for chaos to demonstrate whether or not chaos exists in the system. In order to stop the system's chaotic trajectory, we ultimately employ a hybrid control method. [ABSTRACT FROM AUTHOR]

We investigate a discrete-time Chen system. First, we give the topological classifications of the fixed points of this system. Then, we analytically show that the discrete Chen system underlies a Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. We confirm the existence of a PD and NS bifurcation via the explicit PD-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory. We performed numerical simulations to confirm our analytical results. Furthermore, we use the 0-1 chaos test to quantify whether there is chaos in the system or not. At the end, the hybrid control strategy and the OGY (Ott, Grebogi, and Yorke) method are applied to eliminate chaotic trajectories of the system. [ABSTRACT FROM AUTHOR]

In this work. we consider an eco-epidemiological model with disease in prey. The role of alternative food is being investigated. Alternative food source for predator is another significant component in the interaction of ecological species and incorporation of this aspect in eco-epidemiological investigations may give some fascinating outcomes. The contribution of this paper is to consider different competition coefficients within the prey population. which leads to the emergent carrying capacity. The pernianence and uniform persistence are established. Moreover. we discuss the local and global stability analysis. For bifurcation analysis. the transmission rate has been taken as parameter. The Hopf bifurcation analysis around the endemic equilibrium point is discussed. Further. we also pay attention to the chaotic dynamics which is produced by the disease. At the end. extensive numerical simulations are performed to demonstrate the effectiveness of our hypothetical outcomes. The numerical simulations reveal that the three species eco-epidemiological system induced chaos when disease spreads iii low level. If we increase the force of infection. then the system shows stable focus through chaos to period-double. period-double to limit cycle. We conclude that chaotic dynamics can be coiitrolled by the alternative food as well as the competition coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we explore local dynamic characteristics, bifurcations and control in the discrete activator-inhibitor system. More specifically, it is proved that discrete-time activator-inhibitor system has an interior equilibrium solution. Then, by using linear stability theory, local dynamics with different topological classifications for the interior equilibrium solution are investigated. It is investigated that for the interior equilibrium solution, discrete activator-inhibitor system undergoes Neimark-Sacker and flip bifurcations. Further chaos control is studied by the feedback control method. Finally, numerical simulations are presented to validate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present a 4D hyperchaotic Rabinovich system which obtained by adding a linear controller to 3D Rabinovich system. Based on theoretical analysis and numerical simulations, the rich dynamical phenomena such as boundedness, dissipativity and invariance, equilibria and their stability, chaos and hyperchaos are studied. In addition, the Hopf bifurcation at the zero equilibrium point of the 4D Rabinovich system is investigated. The numerical simulations, including phase diagrams, Lyapunov exponent spectrum, bifurcations, power spectrum and Poincaré maps, are carried out in order to analyze and verify the complex phenomena of the 4D Rabinovich system. [ABSTRACT FROM AUTHOR]

This paper presents a new four-dimensional (4D) hyperchaotic system by introducing a linear controller to 3D chaotic Qi system. Based on theoretical analysis and numerical simulations, the dynamical behaviors of the new system are studied including dissipativity and invariance, equilibria and their stability, quasi-periodic orbits, chaotic and hyperchaotic attractors. In addition, the Hopf bifurcation at the zero equilibrium point and hyperchaos control of the system are investigated. The numerical simulations, including phase diagram, Lyapunov exponent spectrum, bifurcations and Poincar'e maps are carried out in order to analyze and verify the complex phenomena of the 4D hyperchaotic system. [ABSTRACT FROM AUTHOR]

At present, stochastic resonance (SR) based on Duffing and Langevin equations has been widely studied, but there is little research on SR phenomenon in higher-dimensional fractional-order systems. Based on the fractional-order Lorenz-like system, the SR phenomenon is studied from the perspective of equilibrium point in this paper. The dynamic process of SR phenomenon is presented, and several key parameters are derived. The results of numerical simulation show that the boundary of SR and chaos system will be broken if the order of the fractional-order system or internal parameters is properly adjusted, and the effect of SR phenomenon will also be influenced. This paper connects two important nonlinear phenomena (chaos and SR) based on the fractional-order system, which provides a new idea for the conversion between chaos and SR systems. [ABSTRACT FROM AUTHOR]

Regarding a nonlinear Zener model with a viscoelastic Maxwell element as the research object, the complicated dynamic behaviors such as homoclinic bifurcation and chaos under harmonic excitation are investigated. At first, the analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on the Melnikov method. Then, the system parameters that meet the analytical condition and the main resonance condition are selected for the numerical simulation. From the bifurcation diagrams and the largest Lyapunov exponents, it is found that the homoclinic orbit breaks, and the system goes to chaos in a crisis way when the excitation amplitude passes the first threshold. The system enters another new chaotic state in the form of period-doubling bifurcation with the increase of the excitation amplitude. At last, the effects of nonlinear term, stiffness coefficient and damping coefficient of Maxwell element on the analytically necessary condition for chaos are analyzed, respectively, and the correctness of the analytical result is proved by numerical simulation. The research result shows that the critical excitation amplitude decreases with the increase of nonlinear term. In addition, the chaotic threshold increases first and then tends to remain unchanged with the raise of stiffness coefficient. The chaotic threshold increases first and then decreases with the enhancement of damping. These results provide a theoretical basis for the research of nonlinear viscoelastic system in the future. [ABSTRACT FROM AUTHOR]

In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold curve is obtained by calculation and numerical simulation. The accuracy of the analytical result is proved by some typical numerical simulation results, including the local bifurcation diagrams, phase portraits, Poincaré maps, and the largest Lyapunov exponents. The effects of excitation frequency and time delay of the displacement feedback are analytically discussed. It could be found that the critical excitation amplitude will increase obviously with the increase of the excitation frequency, and under the selection of certain parameters, the critical excitation amplitude takes the time delay of 0.58 as the inflection point, which decreases at first and then increases. [ABSTRACT FROM AUTHOR]

In this paper, we study a dual-channel closed-loop supply chain (CLSC) consisting of one manufacturer, one retailer and one third-party firm or platform (3P). The manufacturer wholesales new products through the traditional retail channel and distributes remanufactured products via 3P. We focus on establishing the dynamic Stackelberg game models for nondelayed and delayed cases, respectively. The existence and local stability of Nash equilibrium are examined as well as the complex dynamical behaviors of each model under various scenarios are investigated by numerical simulations, such as stability region, bifurcations, chaos, strange attractors, and so on. Moreover, the impacts of some key parameters on the performance of chain members are analyzed. In addition, the variable feedback control method is utilized to eliminate the system chaos. The results reveal that the high value of the consumer discount perception for remanufactured products and excessively fast price adjustment speed have a destabilization effect on the Nash equilibrium point. In addition, adopting delay decisions by manufacturer does not always make the system more stable because it can exert either positive or negative effect on the system's stability, while an intermediate delay weight is conducive to the system have a higher chance to stay stable. Furthermore, the manufacturer's profits will be declined significantly while the profits of retailer and 3P will be elevated to some extent when the system falls into periodic and chaotic motions, so chaos is not always necessarily detrimental to all the decision makers in the dual-channel CLSC. [ABSTRACT FROM AUTHOR]

The classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard, the PK parameters area under the curve (AUC) and $C_{\max}$ are obtained for both treatment groups and their geometric mean ratios are considered. According to current guidelines by the U.S. Food and Drug Administration and the European Medicines Agency, the formulations are declared to be sufficiently similar if the $90\%$ confidence interval for these ratios falls between $0.8$ and $1.25 $. As NCA is not a reliable approach in case of sparse designs, a model-based alternative has already been proposed for the estimation of $\rm AUC$ and $C_{\max}$ using nonlinear mixed effects models. Here we propose another, more powerful test than the TOST and demonstrate its superiority through a simulation study both for NCA and model-based approaches. For products with high variability on PK parameters, this method appears to have closer type I errors to the conventionally accepted significance level of $0.05$, suggesting its potential use in situations where conventional bioequivalence analysis is not applicable. [ABSTRACT FROM AUTHOR]

In recent years, encryption technology has been developed rapidly and many image encryption methods have been put forward. The chaos-based image encryption technique is a modern encryption system for images. To encrypt images, it uses random sequence chaos, which is an efficient way to solve the intractable problem of simple and highly protected image encryption. There are, however, some shortcomings in the technique of chaos-based image encryption, such limited accuracy issue. The approach focused on the chaotic system in this paper is to construct a dynamic IP permutation and S-Box substitution by following steps. First of all, use of a new IP table for more diffusion of all image pixels based on a 1D logistic map to build IP table. Secondly, a new S-Box based on 2D-Henon chaos was created using more confusion to replace G-channel image data. Finally, design of a modern image encryption approach. This approach uses the key process confusion and diffusion operation and depend on IP and S-Box proposals in the encryption process and several shuffling operations using the 3D- Lornez chaos theory. Theoretical research and simulation suggest that starting sensitivity value of this method is high, has high protection, and encryption speed. Moreover, it also holds the value of the neighboring RGB close to zero. The studies show that the information security capabilities would be both safer and more efficient, as a result of our image quality assessment study. Number of Differential Pixel Rate Change Attacks (NPSR), Unified Average Altered Intensity (UACI), are quality and strength of encryption processing are proved by pixel correlation, Entropy to be good results. [ABSTRACT FROM AUTHOR]

Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fish chaotic system. First, we derived the existence of a chaotic attractor in the fractional-order system and also synchronisation problem between two identical fractional-order chaotic systems is studied. Also, control design for the synchronisation with a suitable linear controller is tested in the response system. Finally, numerical simulation results are provided to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article investigates a prey–predator model incorporating a novel refuge proportional to prey and inverse proportion to the predator. We find conditions for the local asymptotic stability of fixed points of the proposed prey–predator model. This article presents Neimark–Sacker bifurcation (NSB) and period‐doubling bifurcation (PDB) at particular parameter values for positive equilibrium points of the proposed refuge‐based prey–predator system. The system exhibits the chaotic dynamics at increasing values of the bifurcation parameter. The hybrid control methodology will control the chaos of the proposed prey–predator dynamical system and discuss the chaotic situation for different biological parameters through graphical analysis. Numerical simulations support the theoretical outcome and long‐term chaotic behavior over a broad range of parameters. [ABSTRACT FROM AUTHOR]

This paper is devoted to study dynamical behaviours of the fractional-order BazykinBerezovskaya model and its discretization. The fractional derivative has been described in the Caputo sense. We show that the discretized system, exhibits more complicated dynamical behaviours than its corresponding fractional-order model. Specially, in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen. In the final part, some numerical simulations verify the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting. [ABSTRACT FROM AUTHOR]

Based on the existing financial system risk models, a set of time-lag financial system risk models is established considering the influence brought by time-lag factors on the financial risk system, and the dynamical behavior of this system is analyzed by using chaos theory. Through Matlab simulation, the bifurcation diagram and phase diagram of time-lag risk intensity and control intensity are plotted. The analysis shows that this kind of time-lag financial system risk model has complex dynamic behavior, different motion states will appear when different parameter values are selected, and the time-lag risk intensity parameter also has a very strong influence on the system motion. To ensure the operation of the financial system in a stable state, measures with certain delay effects must be taken to control the risk and to choose the appropriate time-lag control intensity, and too much or too little time-lag control intensity is not conducive to the benign operation of the system. [ABSTRACT FROM AUTHOR]

In this paper, a simple chaotic memristor-based circuit with an external stimulation is proposed, and its basic dynamic properties are demonstrated. When the external perturbation becomes time varying and its frequency is low enough, the system has two-time scales, which can be employed to explore the mechanisms of symmetrical Hopf-induced bursting oscillations and delay effects. Furthermore, delay-times on Hopf-induced bursting at different frequencies of the external stimulation are measured. The results show that the relationship between the delay-time and external frequency is subject to a power law. In order to enhance the existing chaos of the system, a 4D system is developed by adding a nonlinear state feedback controller, which shows hyperchaos under some suitable parameters. These two systems are implemented on Multisim and hardware platforms, and the corresponding experimental results verify the correctness of the numerical simulations. [ABSTRACT FROM AUTHOR]

• Perceptual development evolves in a stereotyped manner, from limited to proficient. • Here, we focus on the functional significance of such developmental progressions. • We review empirical and computational studies of typical and atypical development. • Early perceptual limitations have therein emerged as scaffolds rather than hurdles. • Thus, the developmental sequencing from limited to proficient may be adaptive. Human perceptual development evolves in a stereotyped fashion, with initially limited perceptual capabilities maturing over the months or years following the commencement of sensory experience into robust proficiencies. This review focuses on the functional significance of these developmental progressions. Specifically, we review findings from studies of children who have experienced alterations of early development, as well as results from corresponding computational models, which have recently provided compelling evidence that specific attributes of early sensory experience are likely to be important prerequisites for later developing skills in several perceptual domains such as vision and audition. Notably, the limitations of early sensory experience have therein emerged as scaffolds, rather than hurdles, being causally responsible for the acquisition of later perceptual proficiencies, while dispensing with these limitations has the perhaps counter-intuitive consequence of compromising later development. These results have implications for understanding why normal trajectories of perceptual development are sequenced in the way that they are, help account for the perceptual deficits observed in individuals with atypical histories of sensory development, and serve as guidelines for the creation of more robust and effective training procedures for computational learning systems. [ABSTRACT FROM AUTHOR]

A chaotic parameter-optimized radial basis function (RBF) forecasting model was proposed. The chaos theory was used to obtain the embedded dimension and delay time of the ENPEMF， and the obtained parameters were used to optimize the RBF neural network. Finally， the trained optimized-RBF was utilized to forecast the strength trend of 14 d ENPEMF data. Numerical simulation results show that the improved RBF model could forecast the Rossler time series well with small error. Applying the improved RBF algorithm to the ENPEMF data before Ms7.0 earthquake in Lushan， it can effectively forecast the ENPEMF intensity trend 14 d before earthquake. The forecasting effect and accuracy are significantly better than that of the traditional RBF algorithm， which is expected to provide support for electromagnetic monitoring and analysis before earthquakes and geological disasters. [ABSTRACT FROM AUTHOR]

In this paper, a novel chaotic new three-dimensional system has been studied by Zhang et al. in 2012. In the system, there are three control parameters and three different nonlinear terms which governed equations. Zhang et al. studied elementary (preliminary) dynamic properties of the chaotic new three-dimensional system by means of bifurcation diagram, maximum Lyapunov exponent, phase portraits, dynamics behaviors by changing some parameters etc., using all possible theoretical analysis and numerical simulation. In this paper, we have demonstrated its complete synchronization. The proposed results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs' rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control. [ABSTRACT FROM AUTHOR]

In this research, we use the double-delayed feedback control (DDFC) method in order to control chaos in a finance system. Taking delays as parameters, the dynamic behavior of the system is investigated. Firstly, we study the local stability of equilibrium and the existence of local Hopf bifurcations. It can find that the delays can make chaos disappear and generate a stable equilibrium or periodic solution, which means the effectiveness of DDFC method. By using the normal form theory and center manifold argument, one derives the explicit algorithm for determining the properties of bifurcation. In addition, we also apply some mathematical methods (stability crossing curves) to show the stability changes of the financial system in two parameters' τ 1 , τ 2 plane. Finally, we give some numerical simulations by Matlab Microsoft to show the validity of theoretical analyses. [ABSTRACT FROM AUTHOR]

In this paper, computer assisted proofs in dynamics (CAPD) group and conventional dynamic analysis methods are applied to find the parameters that make the brushless DC motor (BLDCM) system chaotic. For the purpose to make the BLDCM system exponentially stable, four simple controllers with just one state variable are proposed, which means that it only needs one sensor instead of two or more in practice. Numerical simulations show that the motor with the new controllers can converge efficiently. Finally, the topological horseshoe theory is introduced to verify the existence of chaos in BLDCM system. [ABSTRACT FROM AUTHOR]

A novel nonlinear fractional order sliding mode controller is proposed to control the chaotic atomic force microscope system in presence of uncertainties and disturbances. In the design of the suggested fractional order controller, conformable fractional order derivative is applied. The stability of the scheme is proved by means of the Lyapunov theory based on conformable fractional order derivative. The simulation results show the advantages of the designed controller such as fast convergence speed, high accuracy and robustness against uncertainties and disturbances. [ABSTRACT FROM AUTHOR]

The function projective synchronization of chaotic system with a new kind of scaling function is proposed in this paper. In general, the scaling function factor of function projective synchronization is a function of the time variable. However, in this paper, the scaling function factor we discussed is a function of state variable which imply that this kind of synchronization is more complicated. Via modified active control method, the controller of the proposed synchronization is designed, and successfully applies to the four dimensional energy resources system and a new hyperchaotic Chua system. Numerical simulation is presented to show the validity of the controller and the proposed synchronization. [ABSTRACT FROM AUTHOR]

Compressed sensing by random under-sampling has been recently used in the context of energy-efficient moving-target gradient descent localization in wireless sensor networks. The present work investigates the possibility of using deterministic chaos in sensing or acquiring time-of-arrival measurement data instead of randomness. The rationale behind this approach is that the output of a chaos system has been empirically proven to behave as random in just a few steps; the advantage gained is ease of implementation on system hardware. In addition, unlike random-sampling which entails difficulty in signal reconstruction, chaos can be re-generated easily to get back the original signal. On the other hand, chaos can add a security dimension to the system in the sense that it is impossible to re-generate a chaotic sequence unless its parameters are known. The simulations conducted reveal the promising potential of the proposed method in terms of localization error function. The proposed method yielded comparable results to those of the previous work with the additional advantage of being less expensive in hardware design. [ABSTRACT FROM AUTHOR]

Highlights • DNA encoding is introduced into the field of optical encryption. • An optical XOR gate is used to achieve XOR operation in ultra-fast DNA encryption. • The DNA rules used for data encoding are different in each row and column, which enhances the security of system. Abstract We propose an optical image encryption scheme based on the Deoxyribonucleic Acid (DNA) theory and the double random phase encoding (DRPE) technique. The piecewise linear chaotic map (PWLCM) is used to generate key images and random phase masks, and to determine DNA encoding rules. In order to achieve ultra-fast DNA encryption, we propose using an optical exclusive-OR (XOR) gate to achieve XOR operation in DNA encryption. Different plaintexts use different initial values of PWLCM, which are generated by Message Digest Algorithm 5 (MD5). The plaintext is encrypted by two rounds of DNA and then by DRPE to form a ciphertext. Numerical simulation and the analysis of attacks on encrypted image are implemented to demonstrate the security and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract In this work, we further investigate the dynamics of the Genesio-Tesi chaotic system which consists of a relatively simple jerk circuit with a quadratic nonlinearity. We complete and enrich the results obtained by Aceng et al. (2016). For this reason, we focus our interest in multistability generation and chaos synchronization as well. By using simulation software tools like PASCAL compiler, Orcad PSPICE and MATLAB, these properties have been characterized via common nonlinear tools including phase portraits, temporal responses, frequency responses, bifurcation diagrams and maximum lyapunov exponent plots. The analysis shows that the Genesio-Tesi system under consideration is able to exhibit complex and interesting behaviors including period doubling bifurcation, chaos, periodic windows and coexistence of multiple attractors. This latter phenomenon has not been found in previous studies of the Genesio-Tesi oscillator thus merits to be shared. We have also shown that Genesio-Tesi systems in their chaotic states can be synchronized and used for a possible masking of information, thus illustrating its importance in engineering. Numerical findings have been validated through experimental studies. [ABSTRACT FROM AUTHOR]

Bifurcations in Huang's chaotic chemical reactor leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales, and its stability is determined from the resulting normal form and verified by numerical simulations. The dynamically rich range of parameters past the Hopf bifurcation is next explored. In order to bring some order to the search for parameter regimes with more complex dynamics, we employ the recent conjecture of Competitive Modes to find chaotic parameter sets in the large multiparameter space for this system. In addition, it is demonstrated that, by changing the point of view, one may tightly localize the chaotic attractor in shape and location in the phase space by mapping the Competitive Modes surfaces geometrically. Finally, we consider the effect of delay on the system, leading to the suppression of the Hopf bifurcation in some regimes, and also all of the subsequent complex dynamics. In modern terminology, this is an example of Amplitude Death, rather than Oscillation Death, as the complex system dynamics is quenched, with all the variables additionally settling to a fixed point of the original system. [ABSTRACT FROM AUTHOR]

Abstract As for the dynamical networks which consist of some high-dimensional nonlinear systems, the problems that researchers are concerned with are usually the asymptotic convergence on some components (rather than all components) of node's state variables under certain condition. This means that partial component synchronization is more meaningful than identical synchronization in some cases. In this paper, the definition of partial component synchronization is given, and then the problem of partial component synchronization on a class of chaotic dynamical networks is investigated. By using matrix theory, stability theory and the hypothesis that several components in the solution vector of a single uncoupled node are ultimately dissipative, some sufficient conditions on partial component synchronization in the chaotic dynamical networks are derived. Finally, numerical simulations are shown to demonstrate the correctness of the theoretical results. Highlights • Partial component synchronization is a kind of group dynamics behavior weaker than identical synchronization. • In this paper, the definition of partial component synchronization is given, and the stability theory of partial variables is applied to study it. • Several sufficient conditions for partial component synchronization to be realized on the network are derived. [ABSTRACT FROM AUTHOR]

Abstract The Rulkov mapping is a phenomenological model that simulates the changes in the neuronal membrane potential. In this work, we introduce a parametric perturbation in the Rulkov map, that can be related to an unexpected behavior, such as a malfunction of the neuronal membrane due to pathologies. The perturbed system still keeps its main characteristics, which includes periodic behavior followed by chaotic bursts. We verify the existence of a set of periodic regions, known as shrimps, embedded in chaotic attractors in the system with parametric perturbation. Some changes in the phase space, time evolution of the variables and bifurcation diagrams are observed. Finally, we show the extreming curves, which demonstrate how is the organization of the periodic regions in the parameter space. Highlights • Parametric perturbation in the Rulkov mapping. • A model that describes the neuronal membrane potential is studied. • The system presents periodic behavior followed by chaotic bursts. • We show how is the organization of the periodic regions in the parameter space. [ABSTRACT FROM AUTHOR]

In this paper, a Noval chaotic dynamical system is proposed and the basic properties of the system are investigated. Linear feedback control technique is used to suppress chaos. The controlled system is stable under some conditions on the parameters of the system determined by Lyapunov direct method. In addition, a function projective synchronization of two identical Noval system is presented. Lyapunov method of stability is used to prove the asymptotic stability of solutions for the error dynamical system. Numerical simulations results are included to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this paper, analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion are obtained through the generalized harmonic balance method. The stability and bifurcation of the periodic evolutions are determined. The bifurcation tree of period-1 to period-8 evolutions of the Brusselator is presented through frequency-amplitude characteristics. To illustrate the accuracy of the analytical periodic evolutions of the Brusselator, numerical simulations of the stable period-1 to period-8 evolutions are completed. The harmonic amplitude spectrums are presented for the accuracy of the analytical periodic evolution, and each harmonics contribution on the specific periodic evolution can be achieved. This study gives a better understanding of periodic evolutions to chaos in the slowly varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos are clearly demonstrated, which can help one understand a route of periodic evolution to chaos in chemical reaction oscillators. From this study, the generalized harmonic balance method is a good method for slowly varying systems, and such a method provides very accurate solutions of periodic motions in such nonlinear systems. [ABSTRACT FROM AUTHOR]

Abstract In order to detect rail cracks by Acoustic Emission (AE) technology, many researches are carried out based on the theoretical and experimental conditions. However, how to detect the crack signals in real noise environment of railway is a key problem for actual application, which has few researches. In this paper, AE detection of rail cracks in real noise environment is investigated and an improved method is proposed to increase the accuracy of crack detection. The AE noise signals are acquired from real operation conditions. They are analyzed and reconstructed by chaos theory. Based on the reconstructed vectors, a reasonable Nonlinear AutoRegressive with eXogenous input (NARX) model of AE noises is built to eliminate noises. For suppressing the abnormal noise interference, a feature detection method is proposed to improve the detection accuracy based on the fused features. Meanwhile, the detection ability of the proposed method is further verified by a longer signal. The results illustrate that the proposed method is effective to detect crack signals in real noise environment. Moreover, the actual application of the proposed method is also discussed and it can provide a useful guidance for AE detection of rail cracks. Highlights • AE detection of rail crack is investigated in real noise environment of railway. • An improved method is proposed to increase the detection accuracy of crack signal. • Generation system of simulated crack signal is designed for nondestructive research. • NARX model is built to eliminate normal AE noises by Chaos theory. • The fused features are employed to suppress abnormal AE noises. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the synchronization between two non-identical 4-D hyperchaotic systems. The nonlinear control technique is used for synchronization. The stability analysis of the error dynamics system is done by (i) Lyapunov's second method and (ii) Cardano's method. Four different expressions of the controller are presented in the paper and a comparison between the two methods are given. We notice that the Cardano's method is better than the Lyapunov approach. Finally, theoretical and numerical simulations are given to illustrate and verify the results. [ABSTRACT FROM AUTHOR]

Abstract This work presents a design of interval type-2 fuzzy brain emotional learning control (T2FBELC) combining with the self-evolving algorithm to help the network to automatically achieve the optimum construction from the empty initial rule. In the control system design, the T2FBELC is the main controller used to mimic an ideal controller, and a robust controller is a compensator for the compensation of the residual error. Implementing the steepest descent gradient approach, the parameter adaptive laws of the proposed system are derived. Besides, the particle swarm optimization (PSO) is applied to find the optimal learning rates for the parameter adaptive laws. The stability of the proposed algorithm is guaranteed using the Lyapunov function. Finally, the effectiveness of the proposed control system is verified by numerical simulations of the chaotic systems. Highlights • The T2FBELC network construction is optimized using the self-evolving algorithm. • The parameter adaptive laws are derived using the steepest descent gradient approach. • The learning rates for the adaptive laws are optimized using the PSO algorithm. • The stability of the proposed algorithm is guaranteed using the Lyapunov function. • The system effectiveness is verified by numerical simulations of the chaotic systems. [ABSTRACT FROM AUTHOR]

This paper presents a novel 3D fractional-ordered chaotic system. The dynamical behavior of this system is investigated. An analog circuit diagram is designed for generating strange attractors. Results have been observed using Electronic Workbench Multisim software, they demonstrate that the fractional-ordered nonlinear chaotic attractors exist in this new system. Moreover, they agree very well with those obtained by numerical simulations. [ABSTRACT FROM AUTHOR]

Ambient sounds arise from a massive superposition of chaotic events distributed over a large area or volume, such as waves breaking on a beach or rain hitting the ground. The directionality and loudness of these sounds as they propagate in complex 3D scenes vary with listener location, providing cues that distinguish indoors from outdoors and reveal portals and occluders. We show that ambient sources can be approximated using an ideal notion of spatio-temporal incoherence and develop a lightweight technique to capture their global propagation effects. Our approach precomputes a single FDTD simulation using a sustained source signal whose phase is randomized over frequency and source extent. It then extracts a spherical harmonic encoding of the resulting steady-state distribution of power over direction and position in the scene using an efficient flux density formulation. The resulting parameter fields are smooth and compressible, requiring only a few MB of memory per extended source. We also present a fast binaural rendering technique that exploits phase incoherence to reduce filtering cost. [ABSTRACT FROM AUTHOR]

A chaos particle swarm optimization (CPSO) algorithm based on the chaos operator (CS) is proposed for global optimization problems and parameter inversion of the nonlinear sun shadow model in our study. The CPSO algorithm combines the local search ability of CS and the global search ability of PSO algorithm. The CPSO algorithm can not only solve the global optimization problems effectively, but also address the parameter inversion problems of the date of sun shadow model location successfully. The results of numerical experiment and simulation experiment show that the CPSO algorithm has higher accuracy and faster convergence than the-state-of-the-art techniques. It can effectively improve the computing accuracy and computing efficiency of the global optimization problems, and also provide a novel method to solve the problems of integer parameter inversion in real life. [ABSTRACT FROM AUTHOR]

This article deals with the dynamical analysis of discrete-time Brusselator models. Euler’s forward and nonstandard difference schemes are implemented for discretization of Brusselator system. We investigate the local dynamics related to equilibria of both discrete-time models. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. A novel chaos control method is implemented in order to control chaos in discrete-time Brusselator models under the influence of flip and Hopf bifurcations. Numerical simulations are provided to illustrate theoretical discussion and effectiveness of newly introduced chaos control strategy. [ABSTRACT FROM AUTHOR]

In this work, we aimed to solve the control regulation problem for a generalized second-order underactuated linear system in order to induce a periodic or chaotic behavior or to cancel the external perturbations, generated by an exogenous system, in the nonactuated coordinate. Further, we showed that, in some cases, it is possible to bring to zero the regulation output errors of the underactuated linear plant, depending on the structure of the plant itself and the exogenous system. In the first stage, the solution was developed for the ideal scenario, in which the whole states of the plant and of the exogenous system were available. Secondly, we showed that in some cases it was possible to solve the regulation output problem when only the observable plant output was measurable. That is, the whole plant state and the exogenous signal could be recovered, if some assumptions were fulfilled. The Lyapunov method was used to perform the stability analysis. The proposed solution was assessed through numerical simulations. [ABSTRACT FROM AUTHOR]