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Abstract In this paper, we construct a duopoly model of technological innovation based on constant conjectural variation under the assumption of bounded rationality. The equilibrium points of constant conjectural variation and their local stability are investigated. By the theoretical proof, we prove that the model displays Li-Yorke chaos and distributional chaos in the ranges of the output adjusted coefficients by employing the snap-back repeller theory. The technological innovation is the main source of the core competitiveness of a firm, and technological content is an important factor of technological innovation. We find that the firms have the optimal technological contents while they could have the maximal profits in the two different situations, non-cooperative technological innovation and cooperative technological innovation. It's proved that the cooperation of technological innovation can increase the marginal technological content, and benefit to technological progress. Then Numerical simulations are used to illustrate the dynamic analysis of the model under the situations with different technological innovation and conjectural variation. When the output adjusted coefficient changes, a series of complex phenomena including bifurcation, chaos and strange attractor can be observed in our model. And when the technological content is larger, the chaos of the system finally appears. [ABSTRACT FROM AUTHOR]

Highlights • A novel no-equilibrium Jerk-like chaotic system is constructed and explored. • The system generates various asymmetric coexisting hidden attractors. • Transient chaos, periodic bursting oscillation and transient periodic bursting oscillation behaviors are obtained. • The unique phenomenon of one to two full Feigenbaum remerging trees is also observed. • The hardware experimental results are performed to prove the numerical simulations. Abstract The topic associated with hidden attractor and multistability has been received considerable attention recently. In this paper, a novel no-equilibrium Jerk-like chaotic system is constructed and explored. Particularly, owing to the absence of the equilibria, such a new system can be categorized as a system with hidden attractors. More interestingly, this system holds three conspicuous characteristics. The first one is that various asymmetric coexisting hidden attractors and complicated transient chaos behaviors are obtained. The second one is the new finding of the periodic bursting oscillation and unusual phenomenon of transient periodic bursting oscillation in the system. The third one is the observation of the amazing and rare phenomenon of one to two full Feigenbaum remerging trees, namely, antimonotonicity. To the best knowledge of us, the last two special features are first discovered and have never been reported, especially in such no-equilibrium chaotic system that exhibits hidden attractors. With the help of phase portraits, time series, bifurcation diagram, Lyapunov exponents, chaotic dynamical diagram, basin of attraction and so forth, the rich hidden dynamical properties of this system are systematically analyzed and investigated. Additionally, a hardware electronic circuit on a breadboard is carried out. A very good similarity between the hardware experimental results and the theoretical analysis testifies the feasibility and practicality of this original system. [ABSTRACT FROM AUTHOR]

Abstract Time-delay is frequently encountered in a variety of practical chaotic systems, such as chaos-communication. The behaviours of time-delay chaotic system are greatly different from those of the original system. Self-time-delay synchronization (STDS) implies that the synchronization between the time-delay system and the original system while maintaining the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. Firstly, we investigate the characteristics of two-time-delay complex Lorenz system. Then we take one-time-delay and two-time-delay complex Lorenz system as examples, and design their controllers to realize STDS. One-time-delay complex Lorenz system is a special case of two-time-delay. Numerical simulations verify the validity of the STDS controllers. The controllers only involve error, and it is easy to realize in practice. Moreover, the time-delay chaotic system exhibits highly stochastic behaviors and unpredictable properties, which can be applied to chaos-communication and enhance the security of communication. [ABSTRACT FROM AUTHOR]

Highlights • Equilibrium points and asymptotic stability. • Uniqueness and existence of solution of the model. • Existence of solutions for 5-D hyperchaotic system with four wings. • Numerical simulations. • Conclusion. Abstract A new 5-D hyperchaotic system with four wings is studied in the light of the newly introduced operator by Atangana and Baleanu with non-local and non-singular fading memory. The basic properties and stability analysis are studied. Picard–Lindelof method is used to examine the existence and uniqueness of solutions of the new 5-D hyperchaotic system with four wings. The numerical simulation results depict a new chaotic behaviours with the ABC numerical scheme. [ABSTRACT FROM AUTHOR]

In this contribution, a new four-wing chaotic system with a smooth piecewise quadratic nonlinearity is introduced. The novel system is inspired from the cubic one introduced by Sampath et al. (2015). Fundamental properties of the new system are discussed and its complex behaviors are characterized using classical nonlinear diagnostic tools. This system exhibits a rich repertoire of dynamic behaviors when suitable set of parameters are chosen including a single two-wing and four-wing chaotic attractors. Further analysis of the novel system shows that four disconnected coexisting stable states can be observed with different initial values. Moreover, the smooth quadratic nonlinearity is easily implemented by using off-the-shelf electronic components (instead of analog multiplier ship in the case of a cubic nonlinearity). The synchronization and the feasibility of the proposed mathematical model are also presented by developing an adaptive synchronization scheme of two identical four-wing chaotic systems and using PSpice simulations based on an electronic analog of the model. [ABSTRACT FROM AUTHOR]

A new fast image cryptosystem was studied in this paper. The system employed the piecewise linear chaotic map and cubic S-box to generate key stream with excellent statistical characteristics for image encryption. Unlike most existing image cryptosystems, the proposed image cryptosystem possessed identical encryption process and decryption process, which both include one key stream generator, two plaintext-unrelated diffusion operations, one plaintext- related confusion operation and one 180-degree matrix rotation operation. To measure the visual difference between the two images of the same size, a new index named BACI (blocked average changing intensity) was presented as the index of sensitivity analysis. Simulate test and comparative analysis show that the proposed image cryptosystem has the characteristics of large key space, fast encryption/decryption speed, high sensitivity, good statistical properties of cipher-text, and etc. The proposed cryptosystem is an available alternative scheme for the practical secure communications. [ABSTRACT FROM AUTHOR]

In the real life, we often simultaneously encounter various social dilemmas, which are also inclined to be voluntarily participated in, instead of previous assumption's compulsory participation in. Accounting on this realistic scenario, we have introduced the mechanism that the individuals have access to different payoff matrices corresponding to different social dilemmas to participate in the multigame with three strategies to choose, including cooperation, defection, going it alone. Furthermore, we set a proportion ψ /2 of the population to play the Prisoner's Dilemma, a proportion ψ /2 of the population to play Snowdrift and a proportion 1 − ψ of the population to play the weak Prisoner's Dilemma, which results in the fact that the mean payoff matrix returns to the basic weak PD. Though numerical simulations, we find that for the smaller temptation to defect, the cooperation can be enhanced by the diversity of the sucker's payoff in the multigame contrast to the basic case. In addition, when the contribution of sucker's payoff is larger or more players choose to play the Prisoner's Dilemma and Snowdrift, the cooperators become more dominated. [ABSTRACT FROM AUTHOR]

In this paper, adaptive control of complicated chaotic systems with unknown parameters is discussed via a set of fuzzy modeling-based adaptive strategy. The proposed fuzzy model theory aims to adjust the inner-weighting of each linear sub-equation, simplize the complicated modeling process, and to reveal the similar behaviors of complicated nonlinear dynamic system. Further, based on the modeling concept, a set of fuzzy model-based adaptive control scheme and its creative fuzzy update laws of parameters are proposed to achieve the goal of adaptive synchronization. Two identical complicated dynamic systems, Mathieu-Van der pol system (M-V system) with uncertainties, are designed and illustrated for numerical simulation example to show the effectiveness and feasibility of the proposed novel adaptive control strategy. [ABSTRACT FROM AUTHOR]

This research investigates pattern self-organization along the route to chaos in a space- and time-discrete predator–prey system, where the prey shows convection movement in space. Through analysis on Turing instability of the system, pattern self-organization conditions are determined. Based on the conditions, simulations are performed under two initial conditions, demonstrating two pattern transitions along the route to chaos. In the first pattern transition, the patterns start from regular stripes, experiencing twisted stripes, then return to regular stripes again. The second pattern transition is much more complex and shows three stages. Especially, an alternation between ordered patterns and disordered chaos is found, contributing greatly to the spatiotemporal complexity of the system. When the system stays at the homogeneous chaotic states, Turing instability driven by convection and diffusion can still force the self-organization of regular striped patterns. The finding in this research provides a new comprehending for pattern self-organization and transition in spatially extended predator–prey systems. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy method is combined with intermittent control method to realize synchronization of chaotic system. Two plant rules of intermittent control are considered to get two theorems. Fuzzy scheme for synchronization is proposed in theorem. Finally, a simulation example is proposed to verify the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper proposes an approach for constructing and generating chaos from a class of three-dimensional linear switching systems via a heteroclinic loop based on the Shilnikov criterion. First, the existence of a switching rule for the system is derived by utilizing the Shilnikov heteroclinic criterion. Then a general design philosophy and its procedure of switching rule are provided to ensure that the proposed approach is applicable to engineering. Two numerical examples are presented to validate the main principle and the implementability of the scheme. Theoretical analysis and numerical simulation are used to demonstrate the feasibility and effectiveness of developed techniques. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an extended model for the prey-predator-scavenger in presence of harvesting to study the effects of harvesting of predator as well as scavenger. The positivity, boundedness and persistence conditions are derived for the proposed model. The model undergoes a Hopf-bifurcation around the co-existing equilibrium point. It is also observed that the model is capable of exhibiting period doubling route to chaos. It is pointed out that a suitable amount of harvesting of predator can control the chaotic dynamics and make the system stable. An extensive numerical simulation is performed to validate the analytic findings. The associated control problem for the proposed model has been analyzed for optimal harvesting. [ABSTRACT FROM AUTHOR]

In the present paper the study of the two-dimensional flow field past a circular cylinder for Reynolds number up to 5 · 10 5 is addressed. A Lagrangian particle method approach has been exploited and the simulations have been performed with high spatial resolutions in order to resolve all the main vortical scales. Long simulation time evolutions have been performed in order to get the vortex shedding dynamics as well as the Fourier analysis of the loads. The adopted numerical method allows to discuss both local (boundary layer and near wake dynamics) and global (far wake dynamics) aspects of the problem.The fundamental aspects related to the different identified flow states as well as the drag crisis mechanism are investigated. [ABSTRACT FROM AUTHOR]

Based on the generalized Hamiltonian system, a new method for constructing a class of three-dimensional (3-D) chaotic systems is presented in this paper. After choosing the proper parameters of skew-symmetric matrix, dissipative matrix and external input, one smooth 3-D chaotic system is proposed to show the effectiveness of the proposed method. Numerical simulation techniques, including phase portraits, Poincaré sections, Lyapunov exponents and bifurcation diagram, illustrate that the proposed 3-D system has periodic, quasi-periodic and chaotic flows under the conditions of different parameters. [ABSTRACT FROM AUTHOR]

In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems. [ABSTRACT FROM AUTHOR]

Using both analytical and numerical methods, global dynamics including subharmonic bifurcations and chaotic motions for a class of inverted pendulum system are investigated in this paper. The expressions of the heteroclinic orbits and periodic orbits are obtained analytically. Chaos arising from heteroclinic intersections is studied with the Melnikov method. The critical curves separating the chaotic and non-chaotic regions are obtained. The conditions for subharmonic bifurcations are also obtained. It is proved that the system can be chaotically excited through finite subharmonic bifurcations. Some new dynamical phenomena are presented. Numerical simulations are given, which verify the analytical results. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem of a class of fractional order chaotic systems. The analytically obtained control structure, derived by blending the systematic backstepping procedure with Mittag-Leffler and Lyapunov stability results, helps in obtaining stability of a special case of strict feedback class of fractional order chaotic systems and at the same time avoids the singularity problem. The stabilizing controller is derived for a class of three dimensional systems which can be expressed in strict-feedback form. Thereafter, the methodology has been applied to two example systems i.e. chaotic Lorenz system and Lü system belonging to the addressed class to show the application of results. Numerical simulation results given at the end confirm the efficacy of the scheme presented here. [ABSTRACT FROM AUTHOR]

In the present paper, the synchronization by the Ge-Yao-Chen (GYC) partial region stability theory of chaotic Mathieu-Van der Pol and chaotic Duffing-Van der Pol systems with fractional order-derivative is proposed. Numerical simulations show that this synchronization technique is very effective and it turns out that the fractional order-derivative induces quick synchronization compared to integer order-derivative of these systems. In order to bring out the chaotic behavior of these systems either with fractional or with integer order-derivative, we simulate their phase portraits and the Lyapunov exponent. Moreover, we provide in this work an approximated solution to both systems to show that the solution of such a system can be represented as a simple power-series function. Furthermore, the representation of the error dynamics with respect to the time before and after the control action approves the effectiveness of the control method and proves the possibility of stabilization and controllability of chaotic systems with an appropriate. Furthermore, the synchronization of the fractional Mathieu-Van der Pol system using the fractional Duffing-Van der Pol system is simulated. [ABSTRACT FROM AUTHOR]

We report the dynamics of a low dimensional fractional order forced LCR circuit using Chua’s diode. The stability analysis is performed for each segment of the piecewise linear curve of Chua’s diode and the conditions for the oscillation and double scroll chaos are obtained. The effect of fractional order on the bifurcation points are studied with the help of bifurcation diagrams. We consider both the derivatives of the systems current and voltage as fractional derivatives. When the order of the derivatives is decreased, the system exhibits interesting dynamical behavior. For instance, the value of the fractional order corresponding to the voltage is decreased, the chaotic regime in the system decreases. But in the case of current, the chaotic regime in the system increases initially and beyond a certain value of order, the chaotic regime decreases and extinguishes from the system. We found the lowest order for exhibiting chaos in the fractional order of the circuit as 2.1. For the first time, the experimental analogue of our proposed system is made by using the frequency domain approximation. The results are obtained from the experimental observations are compared with numerical simulations and found that they match closely with each other. The existence of chaos in the circuit is analyzed with the help of 0-1 test and power spectrum. [ABSTRACT FROM AUTHOR]

This paper presents a new method of controlling a unified chaotic system by using output feedback control strategy. In particular, for an arbitrarily given equilibrium point of a unified chaotic system, we design explicit and simple output feedback control laws by which the equilibrium point is globally and exponentially stabilized. Computer simulations are employed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

By utilizing a memristor to substitute a coupling resistor in the realization circuit of a three-dimensional chaotic system having one saddle and two stable node-foci, a novel memristive hyperchaotic system with coexisting infinitely many hidden attractors is presented. The memristive system does not display any equilibrium, but can exhibit hyperchaotic, chaotic, and periodic dynamics as well as transient hyperchaos. In particular, the phenomenon of extreme multistability with hidden oscillation is revealed and the coexistence of infinitely many hidden attractors is observed. The results illustrate that the long term dynamical behavior closely depends on the memristor initial condition thus leading to the emergence of hidden extreme multistability in the memristive hyperchaotic system. Additionally, hardware experiments and PSIM circuit simulations are performed to verify numerical simulations. [ABSTRACT FROM AUTHOR]

A discrete predator-prey system with square root functional response is presented. We study the existence and local stability analysis of the system. The conditions of existence of flip and Niemark-Sacker bifurcations in the system are derived. Furthermore, the chaotic behavior of the system in the sense of Marotto is proved. Numerical simulations are performed to show the consistence with analytical results and also to exhibit the complexity of the system. Finally, chaos control in the system is achieved via OGY feedback control method. [ABSTRACT FROM AUTHOR]

In this paper, the spatiotemporal dynamics of a delayed diffusive prey–predator model with nonlinear predator harvesting is investigated. Through mathematical analysis, we obtain the conditions for Turing and Hopf bifurcation. Numerical simulations display a variety of spatial patterns including spots, strips, mixture of spots and strips, spiral, patchy structure, and chaos. The delay is found to have significant influence on the emergent spatial patterns, such as changing arm length and direction of strips, and accelerating the transformation of spatial patterns. [ABSTRACT FROM AUTHOR]

The analysis of circuit employing the Kirchhoff's circuit laws also known as dynamics of Chua's circuit is extended in this work using the newly established fractional derivative with nonlocal and non-singular kernel. A new numerical analysis is presented and used to solve the extended model. Some numerical simulations are done for different values of the fractional order and new chaotic behaviors are obtained. [ABSTRACT FROM AUTHOR]

In recent years, many communication systems that use a function to encode an information in a chaotic signal were proposed. Since every transmission channel is bandlimited in nature, it is required to determine and to control the chaotic signal spectrum. This way, a bandlimited chaos-based communication system (CBCS) was proposed using digital filters and chaotic synchronization. As the filters modify the original chaotic system, it is necessary to study how their insertion affects chaotic synchronization. In this work, we present a digital discrete-time bandlimited CBCS system analysis, considering practical settings encountered in conventional communication systems. The proposed system is based on master–slave chaotic synchronization and the required conditions for its synchronization is obtained analytically for a general K -dimensional chaos generator map. The performance of this system is evaluated in terms of bit error rate. As a way to improve the signal to noise ratio, we also propose to filter the out-of-band noise in the receiver. Numerical simulations show the advantages of using such a scheme. [ABSTRACT FROM AUTHOR]

Stabilizing an unstable equilibrium point in a fractional-order chaotic system is studied using prediction-based feedback method in this paper. Sufficient conditions for stabilization of equilibrium points are explicitly given and rigorously proven. The proposed approach is effective and easy to be implemented, but its application is limited to systems with no external disturbances and uncertainties in the model description. Numerical simulations show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Based on the observance in human society, the satisfaction level of an individual as a result of an obtained payoff depends on personal tendency to some extent; we establish a new model for spatial prisoner’s dilemma games. We describe individual satisfaction as a stochastically deviated value around each of the four payoffs stipulated by a payoff matrix, which is maintained throughout the life of a certain agent. When strategy updating, an agent who refers to his own satisfaction level cannot see neighbors’ satisfaction levels but can only observe neighbors’ accumulated payoffs. By varying the update rule and underlying topology, we perform numerical simulations that reveal cooperation is significantly enhanced by this change. We argue that this enhancement of cooperation is analogous to a stochastic resonance effect, like the payoff noise effects Perc (2006). [ABSTRACT FROM AUTHOR]

This paper aims at studying local and global dynamics in a nonlinear duopoly with quantity-setting firms and non-cooperative advertising investments that affect the degree of (horizontally) differentiated products. It concentrates on persuasive advertising in a model where each firm has limited information and uses a behavioural rule to set the quantity for the subsequent period. By using some mathematical techniques and numerical simulations, our results show the existence of weak (à la Milnor) attractors, multistability and chaotic dynamics. In the long term, firms may continuously shift from states in which they invest in advertising to states in which advertising investment is absent. [ABSTRACT FROM AUTHOR]

A fractional-order permanent magnet synchronous motor (PMSM) model is proposed and analyzed by phase portraits, bifurcation diagrams, Lyapunov exponents and Poincaré maps in this paper. Numerical simulations show that the proposed PMSM model with fractional integral of order α ∈ [ 0.94 , 1 ] is chaotic on the condition of great changes of parameter. Further, through a transfer function approximation of fractional-order operator, an experimental circuit composed of resistors, capacitors, operational amplifiers and analog multipliers is presented to realize the fractional-order PMSM model, and whose chaotic behavior is also recorded by a digital oscilloscope in experiment. [ABSTRACT FROM AUTHOR]

In view of obtaining a larger key space and thus improve the level of security attainable in chaotic communication, this paper examines the dynamics of a switched, fractional-order chaotic system. Taking the fractional-order Chen system as a starting point, the dynamics of a modified version of that system is examined, and the composed system is hereafter realized by allowing switching between the two different subsystems. Our work first demonstrates how fractional-order chaotic systems can be realized physically. For the fractional-order switching chaotic system, a linear feedback controller and a number of synchronization schemes are designed. Our simulations show that control and synchronization of the individual subsystems can be achieved with the same feedback and synchronization controller. [ABSTRACT FROM AUTHOR]

The noise activated dc voltage signal sensor based on Chua’s electronic circuit made from standard electronic components and operating in the chaotic regime where two single scroll attractors coexist is proposed. The crossings between attractors are driven only by the Gaussian noise. The unknown dc target signal is detected and measured via the monitoring of the residence time proportion the sensor stays in one of the two attractors. The dependence of the output time proportion on the input dc target signal voltage and the noise intensity were obtained performing computer simulations. The optimal noise intensity range for detection is indicated and the dependence of the measurement error on the observation time in this range is obtained. The nearly linear output–input relation for the optimal noise level is found. [ABSTRACT FROM AUTHOR]

This paper considers a mixed duopoly competition model, in which two enterprises produce heterogeneous commodities and compete for output in the same market. One enterprise separates the ownership from the management rights, and the enterprise owner entrusts a manager to manage the enterprise. The other enterprise considers consumer surplus. Through stability theory and numerical simulation, the local stability of each equilibrium point and the way the system performs bifurcation are analyzed. By using the basin of attraction, the global stability of the system is studied. The multistability is explained and the properties and some phenomena of the basin of attraction and the chaotic attractor are analyzed by using the knowledge of noninvertible map and critical curve. Finally, the influence of parameters on enterprise profit and objective is also analyzed, which is helpful for enterprises to make decisions in the process of game. • A mixed duopoly Cournot competition model is established based on heterogeneous products. • The complex dynamic behavior of the economic system is analyzed by means of chaos theory and numerical simulation. • The complex structures of the basin of attraction and chaotic attractor are studied by using noninvertible map. • The influence of the parameters on the average objective and the average profit of the two enterprises is analyzed. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to find out how uncertainties in the characterization of magnetic materials propagate through identification and numerical simulation to the computation of iron losses in electrical machines. Design/methodology/approach – The probabilistic uncertainties in the iron losses are modelled with the spectral approach using chaos polynomials. The Sobol indices are used for the global sensitivity analysis. The machine is modelled with a 2D finite element method and the iron losses are computed with a previously developed accurate method. Findings – The uncertainties propagate in different ways to the different components of losses, i.e. eddy current, hysteresis, and excess losses. The propagation is also different depending on the investigated region of the machine, i.e. Stator or rotor teeth, yokes, tooth tips. Research limitations/implications – The method does not account for uncertainties related to the manufacturing process, which might result in even larger variability. Practical implications – A major implication of the findings is that the identification of iron loss parameters at low frequencies does not affect the loss variability. The identification with high-frequency measurement is very important for the rotor tooth tips. The variability in the excess loss parameters is of low impact. Originality/value – The presented results are of importance for the magnetic material manufacturers and the electrical machine designers. The manufacturers can plan the measurement and identification procedures as to minimize the output variability of the parameters. The designers of the machine can use the result and the presented procedures to estimate the variability of their design. [ABSTRACT FROM AUTHOR]

In this paper, chaotic dynamics of the vibro-impact system under bounded noise excitation is investigated by an extended Melnikov method. Firstly, the Melnikov method in the deterministic vibro-impact system is extended to the stochastic case. Then, a typical stochastic Duffing vibro-impact system is given to application. The analytic conditions for occurrence of chaos are derived by using the random Melnikov process in the mean-square-value sense. In addition, the numerical simulations confirm the validity of analytic results. Also, the influences of interesting system parameters on the chaotic dynamics are discussed. [ABSTRACT FROM AUTHOR]

Cournot oligopolies are examined with two kinds of output adjustment costs, which model the use of contingent work force and additional investments. The best responses of the firms are first determined and the partial adjustment toward best responses is assumed in formulating a dynamic model. The steady states are first characterized and the dynamic behavior of the output trajectories is demonstrated by computer simulation. With small number of firms and low speeds of adjustments the trajectories converge to a steady state. This convergence is lost with increasing number of firms and/or larger speeds of adjustment giving the possibility of cycles and even chaotic behavior. [ABSTRACT FROM AUTHOR]

In Aziz-Alaoui (2002) a three species ODE model, based on a modified Leslie–Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in Aziz-Alaoui (2002), if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations. [ABSTRACT FROM AUTHOR]

This paper presents fuzzy model-based design for control and synchronization of chaotic systems. In this framework, the chaotic systems are exactly reproduced based on a Takagi-Sugeno (T-S) fuzzy model. Then the fuzzy controllers for control and synchronization are designed using the predictive method and some new and useful criteria are derived. Finally, numerical simulations are presented to illustrate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

We study secondary instabilities in a coherently driven passive optical fiber cavity. We show that timemodulated solutions which are generated at the onset of instability experience convective and absolute Eckhaus instabilities. The splitting of the secondary instabilities into convective and absolute instabilities drastically impacts the instability boundaries. As a consequence, the stability range of time-modulated waves is enlarged. More importantly, the threshold of absolute instability determines the transition from time-periodic wave trains to a chaotic regime. In the latter the wave trains are composed of irregular oscillations embedded in regular ones. The predictions are in excellent agreement with numerical simulations. [ABSTRACT FROM AUTHOR]

Highlights: [•] Dynamics of a forced periodic Colpitts oscillator (CO) is studied. [•] Forcing signal (periodic or chaotic) is generated in CO by tuning dc bias current. [•] CO forced by periodic signal becomes chaotic through period doubling route. [•] Conditionally phase synchronized chaos is generated for chaotic forcing. [•] Experimental results corroborate findings of numerical simulation. [ABSTRACT FROM AUTHOR]

Highlights: [•] We develop an adaptive synchronization method for a chaotic permanent magnet synchronous motor (PMSM). [•] We show stability and convergence of the system responses. [•] We give simulation results to verify that the proposed method is useful for adaptive synchronization of a chaotic PM synchronous motor under model parameter and load torque variations. [ABSTRACT FROM AUTHOR]

• The nonlinear chaotic complex system are studied. • The ultimate bound of the nonlinear chaotic complex systems are presented. • The obtained solutions are presented by 2D figures. The competitive modes for a nonlinear chaotic complex system are studied in this paper. In hyperchaotic, chaotic, and periodic cases, we examined competitive modes that are a tool for detecting chaos in a system. Also, using an analytical method and Lagrange optimization, we were able to calculate the ultimate bound of the nonlinear chaotic complex systems. We have presented is simpler and more accurate than other methods that implicitly calculate the ultimate bound. The estimation of the explicit ultimate bound can be used to study chaos control and chaos synchronization. Numerical simulations illustrate the analytical results. [ABSTRACT FROM AUTHOR]

• A fractional-ordered Leslie-Gower prey-predator model is studied. Jury stability test is applied to get certain conditions for occurrence of Neimark-Sacker bifurcation, flip bifurcation and fold bifurcation. • A wide range of dynamics viz. periodic solution, quasi periodicity and chaos is obtained. • Three chaos control techniques: State feedback, pole-placement and hybrid control are implemented in order to reduce the complexity of the system. • State feedback and pole-placement technique restore the stability for a certain range of parameters although hybrid control technique works effectively. In this work, a discretized two-dimensional Leslie-Gower prey-predator model is investigated. The results for the existence and uniqueness and the conditions for the local asymptotic stability of the solutions are determined. It is also exhibited that the discrete system undergoes Neimark-Sacker, flip and fold bifurcation under certain conditions. The discretized system exhibits wide range of complex dynamical behavior viz. periodicity, quasi periodicity and chaos with respect to different parameters. Further, three control methods: state feedback, pole-placement and hybrid control are deployed to control the chaos in the system. Under certain conditions, chaos and bifurcation of the system are stabilized through the control strategies. The extensive numerical simulation is done to demonstrate the analytical findings. [ABSTRACT FROM AUTHOR]

The study of chaotic PDEs with variable coefficients involves higher level of complexity than for the ones with constant coefficients. In this paper, we investigate the chaotic oscillations of a one-dimensional second order linear hyperbolic PDE with variable coefficients that is factorizable as a product of two noncommutative first order operators and the boundary conditions at both ends of the PDE are general nonlinear. Numerical simulations are provided to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]