Impulsive Synchronization Research Articles

Impulsive synchronization and initial value effect for a memristor-based chaotic system

Taking Chua's circuit with a smooth cubic flux-controlled memristor as an example, the impulsive control synchronization method for two identical memristor-based chaotic systems is studied. Based on the Lyapunov stability theory, the asymptotic stability condition for the impulsive synchronization of the memristor-based chaotic systems is given. Combining with the maximum conditional Lyapunov exponent spectrum of the error system, effects of the system initial values on the performances of impulsive synchronization are discussed, and corresponding simulation experiments are performed. Results indicate that using impulsive synchronization for the two identical memristor-based chaotic systems is feasible and effective with appropriate impulsive control parameters; the initial values of the memristor-based chaotic systems have some effects on the performances of impulsive synchronization, which can be inhibited by increasing the impulsive coupling strength.

Impulsive Synchronization of Hyperchaotic Lü Systems with Two Methods

In the paper, impulsive synchronization of two hyperchaotic Lu systems with different initial conditions is studied. The sufficient conditions on feedback strength and impulsive distances are established from two different angles to guarantee the synchronization. The relevant theoretical proofs are presented. Numerical simulations show the effectiveness of the methods.

Synchronization of Impulsive Real and Complex Van der Pol Oscillators

Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems, for example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics, etc., do exhibit impulsive effects. In a recent paper [1], both real and complex Van der Pol oscillators were introduced and shown to exhibit chaotic limit cycles and in [2] an active control and chaos synchronization was introduced. In this paper, impulsive synchronization for the real and complex Van der Pol oscillators is systematically investigated. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set of initial conditions, the differences between the master and slave systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Further results on the impulsive synchronization of uncertain complex‐variable chaotic delayed systems

Synchronization and control of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this article, we investigate the problem of impulsive synchronization for the complex‐variable delayed chaotic systems with parameters perturbation and unknown parameters in which the time delay is also included in the impulsive moment. Based on the theories of adaptive control and impulsive control, synchronization schemes are designed to make a class of complex‐variable chaotic delayed systems asymptotically synchronized, and unknown parameters are identified simultaneously in the process of synchronization. Sufficient conditions are derived to synchronize the complex‐variable chaotic systems include delayed impulses. To illustrate the effectiveness of the proposed schemes, several numerical examples are given. © 2014 Wiley Periodicals, Inc. Complexity 21: 131–142, 2016

Adaptive–impulsive synchronization and parameters estimation of chaotic systems with unknown parameters by using discontinuous drive signals

In this paper, adaptive–impulsive synchronization and parameters estimation of chaotic systems only by using discontinuous drive signals are investigated. In the scheme proposed both the impulsive synchronization controller and the adaptive parameters update law are modeled only by using discontinuous output of the chaotic system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. This is meaningful in applications when continuous signals cannot be obtained. Moreover, concrete schemes are designed for quantum cellular neural network (Quantum-CNN) and well known Chen chaotic system. Results show that synchronization and the parameters estimation can be achieved under some conditions. The numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.

The Research of Electronic Transformer Data Synchronization Method Based on Newton Interpolation

Data synchronization of electronic instrument transformer is introduced. Synchronization method commonly used are analyzed in aspects of their advantages and disadvantages, such as interpolation synchronization, impulsive synchronization method; Then, a new approach based on Newton interpolation is presented, and the simulation and error analysis are given. The theoretical analysis results show that this method can reach to the same precision with Lagrange interpolation which is accurate in synchronization of harmonic components and obtain the synchronized data fast. Finally this paper sets equal interval sampling and non-equal interval sampling data, and then calculates maximum error in the case of the steady state and transient state respectively by using Matlab. The simulation results proved the feasibility of this method and its engineering practical value.

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

This article investigates the adaptive impulsive synchronization of delayed chaotic system with full unknown parameters. Aiming at this problem, we propose a new adaptive strategy, in which both the adaptive–impulsive controller and the parameters adaptive laws are designed via the discrete‐time signals from the drive system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. Moreover, the concrete adaptive strategies are achieved for delayed Hopfield neural network, optical Ikeda system and the well‐known delayed Lü chaotic system. As expected, numerical simulations show the effectiveness of the proposed strategy. This method has potential applications in parameters estimation, secure communication, and cryptanalysis when only discrete signals are transmitted in communication channel. © 2014 Wiley Periodicals, Inc. Complexity 21: 43–51, 2016

Pinning impulsive directed coupled delayed dynamical network and its applications

The main objective of the present paper is to further investigate pinning synchronisation of a complex delayed dynamical network with directionally coupling by a single impulsive controller. By developing the analysis procedure of pinning impulsive stability for undirected coupled dynamical network previously, some simple yet general criteria of pinning impulsive synchronisation for such directed coupled network are derived analytically. It is shown that a single impulsive controller can always pin a given directed coupled network to a desired homogenous solution, including an equilibrium point, a periodic orbit, or a chaotic orbit. Subsequently, the theoretical results are illustrated by a directed small-world complex network which is a cellular neural network (CNN) and a directed scale-free complex network with the well-known Hodgkin–Huxley neuron oscillators. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.

Synchronization of a class of chaotic systems using small impulsive signal

In this paper the issue of impulsive synchronization of a class of uncertain chaotic systems with parameters perturbation is investigated. Applying the impulsive theory and linear matrix inequality technique, some less conservative and easily verified criteria for impulsive synchronization of chaotic systems are derived. The proposed impulsive synchronization scheme is applied to the chaotic Murali–Lakshmanan–Chua circuit and hyperchaotic Chen and the corresponding synchronization conditions are derived. Moreover, the boundaries of the stable region are also estimated according to the equidistant impulse interval. The effectiveness of the method is demonstrated by the computer simulation.

Impulsive complex projective synchronization in drive–response complex coupled dynamical networks

This paper investigates the problem of impulsive complex projective synchronization for drive–response complex-variable dynamical networks with complex coupling, and the dynamical networks with and without delayed complex-variable system nodes are considered. According to the stability analysis of the complex-variable impulsive functional differential equation, the sufficient conditions for achieving complex projective synchronization of drive–response network with complex inner and outer couplings are obtained by taking advantage of the Lyapunov function in the complex fields. In addition, the adaptive coupling strength methods are adopted to achieve the complex projective synchronization. Numerical examples are finally presented to illustrate the effectiveness and correctness of the theoretical results.

New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems

This paper studies the robust adaptive-impulsive synchronization in chaotic delayed neural networks with uncertainties. For this class of complex networks, some simple adaptive-impulsive controllers with updated strengths are designed. Using the well-known extended Halany inequality and Lyapunov functions, several less conservative conditions are obtained compared with the existing results. The simulation results show that the proposed results are effective.

Impulsive control and synchronization of nonlinear system with impulse time window

In this paper, the issue on impulsive control and synchronization of nonlinear system with impulse time window are investigated. The considered impulsive effects can be stochastically occurred at a determined time window. Hence, the impulses here can be more general and more applicable than the fixed impulses. Some novel and easy-to-check criteria with impulse time window are obtained to guarantee the impulsive control and synchronization global asymptotical stable. Especially, on the basis of the our analysis, we only choose an efficient impulse time window instead of choosing fixed-impulse sequences. Finally, the simulation results further demonstrate the effectiveness of our theoretical results.

Impulsive practical tracking synchronization of networked uncertain Lagrangian systems without and with time-delays

This paper presents a procedure for studying tracking synchronization of networked Lagrangian systems via impulsive control, where each agent is allowed to be nonidentical, even uncertain dynamics. Some algebraic criteria for tracking synchronization without and with time-delays are established respectively. It turns out that these criteria can provide a novel impulsive control strategy to synchronize globally networked Lagrangian systems to a given time-varying target trajectory with a desired tracking error bound (called as practical tracking synchronization). A distinctive feature of the developed control strategy is fully to take into account the effects of impulsive constraints, and thereby to yield impulsive synchronization motion of networked Lagrangian systems, provided that each agent instantaneously interacts with its neighbors only at some discrete moments. As a direct application of the theoretical results, practical tracking synchronization of nonidentical 3-DOF mobile robots without and with time-delays is discussed in detail. Simulation results illustrate and visualize the effectiveness and feasibility of the proposed control technique.

Impulsive synchronization of time delay bursting neuron systems with unidirectional coupling

In the article, impulsive synchronization of chaotic bursting in Hindmarsh–Rose neuron systems with time delay via partial state signal is investigated. Based on impulsive control theory of dynamical systems, the sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. Numerical simulations show the effectiveness of the proposed scheme. The obtained results may be helpful to understand dynamical mechanism of signal transduction in real neuronal activity. © 2014 Wiley Periodicals, Inc. Complexity 21: 38–46, 2015

Impulsive exponential synchronization of randomly coupled neural networks with Markovian jumping and mixed model-dependent time delays

In this paper, the exponential synchronization problem for an array of N randomly coupled neural networks with Markovian jump and mixed model-dependent time delays via impulsive control is investigated. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and continuous distributed delays. By making use of the Kronecker product and some useful techniques, a novel Lyapunov–Krasovskii functional suitable for handling distributed delays was proposed and then we show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. The results presented in this paper generalize and improve many known results. Two numerical examples are also given to show the effectiveness of the theoretical results.

Chaotic analogue‐to‐information conversion with chaotic state modulation

Chaotic compressive sensing is a non-linear framework for compressive sensing. Along the framework, this study proposes a chaotic analogue-to-information converter, ‘chaotic modulation’, to acquire and reconstruct band-limited sparse analogue signals at sub-Nyquist rate. In the chaotic modulation, the sparse signal is randomised through state modulation of continuous-time chaotic system and one state output is sampled as compressive measurements. The reconstruction is achieved through the estimation of the sparse coefficients with the principle of chaotic impulsive synchronisation and lp -norm regularised non-linear least squares. The concept of supreme local Lyapunov exponents (SLLE) is introduced to study the reconstructablity. It is found that the sparse signals are reconstructable, if the largest SLLE of the error dynamic system is negative. As examples, the Lorenz system and the Liu system excited by sparse multi-tone signals are taken to illustrate the principle and the performance.

A new chaotic system without linear term and its impulsive synchronization

In this paper, a new chaotic system without linear term is presented by ordinary differential equations, and some basic dynamical properties are studied. Moreover, the impulsive synchronization problem of the new chaotic systems is investigated by using uncertain impulsive control matrix. Using the impulsive theory, sufficient conditions are derived for the synchronization of new chaotic systems. Numerical simulation example is provided to verify the effectiveness of the proposed approach.

Impulsive synchronization schemes of stochastic complex networks with switching topology: Average time approach

In this paper, a novel impulsive control law is proposed for synchronization of stochastic discrete complex networks with time delays and switching topologies, where average dwell time and average impulsive interval are taken into account. The side effect of time delays is estimated by Lyapunov–Razumikhin technique, which quantitatively gives the upper bound to increase the rate of Lyapunov function. By considering the compensation of decreasing interval, a better impulsive control law is recast in terms of average dwell time and average impulsive interval. Detailed results from a numerical illustrative example are presented and discussed. Finally, some relevant conclusions are drawn.

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.

Impulsive synchronization of a class of chaotic systems

This paper deals with the impulsive synchronization problem of a class of chaotic systems. By employing the comparison principle and the linear matrix inequalities approach, some less conservative and easily verified sufficient conditions for impulsive synchronization of this class of chaotic systems are derived, these new sufficient conditions can be applied to analyze the impulsive synchronization of the Chua's oscillators. Moreover, the numerical simulation of Chua's oscillators under impulsive control shows the effectiveness of the proposed theory, and obtains better estimation of the boundary of the stable region than the existing approaches.