Generalized chaos synchronization of a weighted complex network with different nodes

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, RSssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.

Estimating the largest Lyapunov exponent in a multibody system with dry friction by using chaos synchronization

Using the properties of chaos synchronization, the method for estimating the largest Lyapunov exponent in a multibody system with dry friction is presented in this paper. The Lagrange equations with multipliers of the systems are given in matrix form, which is adequate for numerical calculation. The approach for calculating the generalized velocity and acceleration of the slider is given to determine slipping or sticking of the slider in the systems. For slip-slip and stick-slip multibody systems, their largest Lyapunov exponents are calculated to characterize their dynamics.

Chaos synchronization in injection-locked semiconductor lasers with optical feedback

Based on the rate equations, we have investigated three types of chaos synchronizations in injection-locked semiconductor lasers with optical feedback. Numerical simulation shows that the synchronization can be realized by the symmetric or asymmetric laser systems. Also, the influence of parameter mismatches on chaos synchronization is investigated, and the results imply that these two lasers can achieve good synchronization, with smaller tolerance of parameter mismatch existing.

Asymptotical p-moment stability of stochastic impulsive differential system and its application to chaos synchronization

In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.

A novel robust proportional-integral (PI) adaptive observer design for chaos synchronization

In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality （LMI）, are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.

Chaos synchronization between two different 4D hyperchaotic Chen systems

This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory~ the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.

Hidden Attractors in a Delayed Memristive Differential System with Fractional Order and Chaos Synchronization

As an important research branch,memristor has attracted a range of scholars to study the property of memristive chaotic systems.Additionally,time⁃delayed systems are considered a significant and newly⁃developing field in modern research.By combining memristor and time⁃delay,a delayed memristive differential system with fractional order is proposed in this paper,which can generate hidden attractors.First,we discussed the dynamics of the proposed system where the parameter was set as the bifurcation parameter,and showed that with the increase of the parameter,the system generated rich chaotic phenomena such as bifurcation,chaos,and hypherchaos.Then we derived adequate and appropriate stability criteria to guarantee the system to achieve synchronization.Lastly,examples were provided to analyze and confirm the influence of parameter a,fractional order q,and time delayτon chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q andτ.

Encoding-decoding message for secure communication based on adaptive chaos synchronization

In this paper, based on an adaptive chaos synchronization scheme, two methods of encoding-decoding message for secure communication are proposed. With the first method, message is directly added to the chaotic signal with parameter uncertainty. In the second method, multi-parameter modulation is used to simultaneously transmit more than one digital message （i.e., the multichannel digital communication） through just a single signal, which switches among various chaotic attractors that differ only subtly. In theory, such a treatment increases the difficulty for the intruder to directly intercept the information, and meanwhile the implementation cost decreases significantly. In addition, numerical results show the methods are robust against weak noise, which implies their practicability.

Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.

Chaos Synchronization on Parameters Adaptive Control for Chen Chaotic System

Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows the synchronization of transmitter systems withreceiver systems even though system parametes are not known to receiver systems.

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

A new color image encryption scheme based on chaos synchronization of time-delay Lorenz system

In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is pro- posed and a lot of coupled items can be taken as zero items to simplify the whole system. A simple linear controller is introduced to realize time-delay chaos synchronization and image encryption. The positions of the image pixels are firstly shuffled and then be hidden in the cartier image. The address codes of the chaotic sequences are adopted to avoid the disturbances induced by the initial value and computer accuracy error. Simulation results for color image are provided to illustrate the effectiveness of the proposed method. It can be seen clearly that the system can converge quickly and the image can be encrypted rapidly.

CHAOS SYNCHRONIZATION OF MORSE OSCILLATOR VIA BACKSTEPPING DESIGN

Synchronization and adaptive synchronization of Morse oscillator with periodic forced section is investigated in this paper. Backstepping design is a recursive procedure that combines the choice of Lyapunov function with the design of controller. The proposed approaches offers a syetematic design procedure for synchronization and adaptive synchronization of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results are presented to show the effectiveness of the approaches.

Delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system

Purpose-The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.Design/methodology/approach-Based on linear matrix inequality and algebra Riccati matrix equation,the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.Findings-A controller is designed and added to the nonlinear system with multiple time-delays.The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme.Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays.Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.Originality/value-The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

Chaos Synchronization between the Coupled Modified Chua's Circuits with Nonlinear Quadratic Function x|x|

This paper studies chaos synchronization in the modified Chua ' s circuitwith nonlinear quadratic function x|x| using a unidirectional Linear coupling approach. A newsufficient condition is derived for chaos synchronization between the two unidirectional coupledmodified Chua ' s circuits with x x I based on the Lyapunov stability theory. A simulation exampleis given for demonstration .

Synchronization of chaotic systems with different orders

A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.

Synchronization between two different chaotic systems with nonlinear feedback control

This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.

Projective synchronization in coupled fractional order chaotic Rossler system and its control

This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.

Controlling projective synchronization coupled chaotic systems

In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Firstly, the synchronizability of the proposed projective synchronization control method is proved mathematically. Then, three different representative examples are discussed to verify the correctness and effectiveness of the proposed control method.