Lag synchronization between discrete chaotic systems with diverse structure

A lag synchronization controller is designed in studying discrete chaotic systems with diverse structures to realize synchronization between Henon and Ikeda sys- terns. The structure of the lag synchronization controller and the error equations of state variables between discrete chaotic systems are presented based on the stability theory. The designed controller has unique structures for different chaotic systems. Lag synchro- nization between any discrete chaotic systems with diverse structures can be achieved. Simulation results show that this control method is effective and feasible.     

Lag synchronization for fuzzy chaotic system based on fuzzy observer

A new fuzzy observer for lag synchronization is given in this paper. By investi- gating synchronization of chaotic systems, the structure of drive-response lag synchronization for fuzzy chaos system based on fuzzy observer is proposed. A new lag synchronization criterion is derived using the Lyapunov stability theorem, in which control gains are obtained under the LMI condition. The proposed approach is applied to the well-known Chen＇s systems. A simulation example is presented to illustrate its effectiveness.     

Anticipating spike synchronization in nonidentical chaotic neurons

Anticipating synchronization is investigated in nonidentical chaotic systems unidirectionally coupled in a master-slave configuration without a time-delay feedback. We show that if the parameters of chaotic master and slave systems are mismatched in such a way that the mean frequency of a free slave system is greater than the mean frequency of a master system, then the phase synchronization regime can be achieved with the advanced phase of the slave system. In chaotic neural systems, this leads to the anticipating spike synchronization: unidirectionally coupled neurons synchronize in such a way that the slave neuron anticipates the chaotic spikes of the master neuron. We demonstrate our findings with coupled Rössler systems as well as with two different models of coupled neurons, namely, the Hindmarsh–Rose neurons and the adaptive exponential integrate-and-fire neurons.     

Lag synchronization of multiple identical Hindmarsh–Rose neuron models coupled in a ring structure

Lag synchronization of multiple identical Hindmarsh–Rose neuron systems coupled in a ring structure is investigated. In the coupled systems, each neuron receives signals only via synaptic strength from the nearest neighbors. Based on the Lyapunov stability theory, the sufficient conditions for synchronization of the multiple systems with chaotic bursting behavior can be obtained. The synchronization condition about the control parameter g is also obtained by numerical method. Finally, numerical simulations are provided to show the effectiveness of the developed methods.     

连续时间系统的混沌同步

本文讨论混沌连续时间系统的完全同步问题，提出一个构造混沌同步系统的新方法。这个方法基于线性系统的稳定性分析准则。通过对系统线性项与非线性项的适当分离，当系统的雅可比矩阵的所有特征值都具有负实部时，同步误差e(t)的线性系统是渐进稳定的，即可实现新系统和原系统的完全同步。新方法不需计算条件Lyapunov指数以作为判定同步的条件，因而比通用方法更为简单有效。新方法适用于自治或非自治系统，尤其适用于具有多于两个正Lyapunov指数的超混沌系统。甚至当初始同步误差极大时，也能实现理想的混沌同步。以Lorenz系统，耦合Duffing振子系统和超混沌Roessler系统作为算例。数值计算结果证实所提出方法的有效性和鲁棒性。     

Diffusive coupling, dissipation, and synchronization

We consider the synchronization of diffusive coupled systems in situations where the synchronization is a consequence of the dissipation in the coupling as well as ones where there is an interaction between the inherent damping in the subsystems and the coupling. It is not required that the subsystems be identical, and they are allowed to have chaotic dynamics. Both discrete and continuous versions are discussed. We also consider coupled oscillators where the dynamics of each oscillator is determined by circuitry across a lossless transmission line.     

Is There Chaotic Synchronization in Space Extend Systems?

Based on coupled map lattice (CML), the chaotic synchronous pattern in space extend systems is discussed. Making use of the criterion for the existence and the conditions of stability, we find an important difference between chaotic and nonchaotic movements in synchronization. A few numerical results are presented.     

Generalized heterochronous synchronization in coupled time-delayed chaotic systems

A new kind of generalized heterochronous synchronization phenomenon is reported. Different kinds of generalized synchronous states (including generalized anticipated, isochronous and lag projective synchronization) coexist among different state variables between two unidirectionally coupled time-delayed chaotic systems. The analytical conditions for generalized heterochronous synchronization are obtained. We also find that the synchronization conditions are independent of the delay times in the original time-delayed system. The theoretical results are well confirmed by the numerical simulations and electronic circuit experiments.     

Influence of the time delay of signal transmission on synchronization conditions in drive-response systems

Conditions for complete and lag synchronizations in drive-response systems are considered under the unified framework of generalized synchronization. The question is addressed that whether the synchronization conditions achieving complete synchronization is still valid for lag synchronization when the time delay of signal transmission between the drive and response systems increases from 0. Theoretical and numerical results show that whether the synchronization conditions is stable for the influence of the time delay of signal transmission depends on a particular form of equilibria of the drive and response systems. Furthermore, it seems that the less the number of the equilibria of the drive system, the more likely the synchronization conditions are stable for the time delay of signal transmission.     

Effect of spatially correlated noise on stochastic synchronization in globally coupled FitzHugh-Nagumo neuron systems

The phenomenon of stochastic synchronization in globally coupled FitzHugh-Nagumo (FHN) neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation (DMA) and direct simulation (DS). Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.     

Adaptive bidirectionally coupled synchronization of?chaotic?systems with unknown parameters

This paper investigates the chaos synchronization of two bidirectionally coupled chaotic systems. In comparison with previous methods (identical bidirectionally coupled synchronization), the present control scheme is different bidirectionally coupled synchronization, which includes different complete bidirectionally coupled synchronization and different partial bidirectionally coupled synchronization. Based on the Lasalle invariance principle, adaptive schemes are designed to make two different bidirectionally coupled chaotic systems asymptotically synchronized, and unknown parameters are identified simultaneously in the process of synchronization. Theoretical analysis and numerical simulations are shown to verify the results.     

Lag quasisynchronization of coupled delayed systems with parameter mismatch by periodically intermittent control

This paper further investigates the lag synchronization of coupled delayed systems with parameter mismatch. Different from the most existing results, we formulate the intermittent control system that governs the dynamics of the synchronization error. As a result of parameter mismatch, complete lag synchronization cannot be achieved. In this paper, a lag quasisynchronization scheme is proposed to ensure that coupled systems are in a state of lag synchronization with an error level. We estimate the error bound of lag synchronization by rigorously theoretical analysis. Numerical simulations are presented to verify the theoretical results.     

Experimental realizations of the HR neuron model with programmable hardware and synchronization applications

This study presents experimental realizations of the HR neuron model with programmable hardware and synchronization applications. The HR neuron model exhibiting burst, spike, and chaotic dynamics has been implemented with both FPAA (Field Programmable Analog Array) and FPGA (Field Programmable Gate Array) devices. These devices provide flexible design possibilities such as reducing the complexity of design, real-time modification, software control and adjustment within the system. And it is also examined experimentally that how the synchronization of two HR neurons are able to achieve by using these hardware. The experimental results obtained from FPAA and FPGA based realizations agree with the numerical simulations very well.     

Synchronization of N different coupled chaotic systems with ring and chain connections

Synchronization of N different coupled chaotic systems with ring and chain Lorenz system, and the R(o)ssler system are used as examples in verifying effectiveness of the method. Based on the Lyapunov stability theory, the form of the controller is designed and the area of the coupling coefficients is determined. Simulations indicate that global synchronization of the N different chaotic systems can be realized by choosing appropriate coupling coefficients by using the controller.     

Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems

The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Synchrony and lag synchrony on a neuron model coupling with time delay

A neuron model of the Morris and Lecar form is investigated, which is composed of two individuals and is considered to be functioned by the gap junction coupling. When the level of the reversal potential in the calcium ion channel is small, neurons adjust their activities to the common asymptotic states. However, if we increase the level of the reversal voltage in the calcium ion channel, the exact synchrony firing of neurons is produced. Patterns of synchrony activity and the stability are observed to vary with the choice of time delay, which also enhances the multi-variety of the spike bursting firing rhythm. The lag synchrony of time trajectories of the voltage is illustrated near the boundary of the synchrony regime.     

Hybrid robust modified function projective lag synchronization in two different dimensional chaotic systems

In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS) in two different dimensional chaotic systems with parameter perturbations, is proposed. In the proposed method, the states of two nonidentical chaotic systems with different orders are asymptotically lag synchronized up to a desired scaling function matrix by means of reduced order and increased order, respectively. Furthermore, based on the reality situation, the parameter perturbations are involved, which are assumed to appear in both drive and response systems. With the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.     

A kind of binary scaling function projective lag synchronization of chaotic systems with stochastic perturbation

This paper investigates a kind of binary function projective lag synchronization of uncertain chaotic systems with stochastic perturbation. In comparison with those of the existing scaling function synchronization, we assume that the given scaling function can be the binary boundary function, even an n-ary boundary function. Based on the LaSalle-type invariance principle for stochastic differential equation, the adaptive control law is derived to make the state of two chaotic systems function projective lag synchronized. Some numerical is also given to show the effectiveness of the proposed method.     

Achievement of chaotic synchronization trajectories of master–slave manipulators with feedback control strategy

This paper addresses a master-slave synchro- nization strategy for complex dynamic systems based on feedback control. This strategy is applied to 3-DOF pla- nar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors. A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors. The dynamical equations of master-slave manipulators with synchronization controller are derived, and the Lyapunov stability theory is used to determine the stability of this controlled synchronization system. In numer- ical experiments, the synchronous motions of end-effectors as well as three joint angles and torques of master-slave manipulators are studied under the control of the proposed synchronization strategy. It is found that the positive gain matrix affects the implementation of synchronization con- trol strategy. This synchronization control strategy proves the synchronization＇s feasibility and controllability for com- plicated motions generated by master-slave manipulators.     

Robust chaos synchronization of fractional-order chaotic systems with unknown parameters and uncertain perturbations

Chaotic systems in practice are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems. Based on Lyapunov stability theory and a fractional-order differential inequality, a modified adaptive control scheme and adaptive laws of parameters are developed to robustly synchronize coupled fractional-order chaotic systems with unknown parameters and uncertain perturbations. This synchronization approach is simple, global and theoretically rigorous. Simulation results for two fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.