Drive-response Synchronization Research Articles

Numerical Simulation of Chaotic Laser Secure Communication

Using the idea of drive-response synchronization, we discuss the principle, numerical simulation of chaotic laser communication. Compared to traditional communications systems, the chaotic laser communication system has a well-kept secret performance, but the chaos synchronization requirements are very strict.

Exponential Synchronization of Delayed Neural Networks With Discontinuous Activations

This paper investigates drive-response synchronization of a class of neural networks with time-varying delays and discontinuous activations. Discontinuous state feedback controller and adaptive controller are designed such that the considered model can realize exponential complete synchronization. Moreover, the convergence rate is explicitly estimated when state feedback control is utilized. The obtained results are also applicable to neural networks with continuous activations since they are a special case of neural networks with discontinuous activations. Results of this paper improve corresponding ones which only quasi-synchronization can be achieved for neural networks with discontinuous activations. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.

Two Synchronization Schemes for Chen Chaotic System

This paper presents two novel synchronization schemes for Chen chaotic system, drive-response synchronization and adaptive synchronization with unknown parameters, numerical simulation results demonstrate the effectiveness of the proposed method.

Adaptive Synchronization of One-Dimensional Discrete Chaotic Systems on Complex Networks

A method of adaptive synchronization of one-dimensional discrete chaotic systems on complex networks is proposed. The nodes of complex networks are constructed by one-dimensional discrete chaotic systems, we consider a general drive-response synchronization model of one-dimensional discrete chaotic systems on complex dynamical networks. Based on the adaptive control technique, the parameter adaptive laws and property conversion laws are given to achieve synchronization and parameters identification simultaneously. Simulation results show that the arithmetic average and geometric mean of all the nodes states are equal, furthermore, the unknown node parameters can be successfully identified, all nodes are transformed to drive nodes. This indicates that chaos synchronization is reached in the whole networks.

A new identification control for generalized Julia sets

In this paper, we propose a new method to realize drive-response system synchronization control and parameter identification for a class of generalized Julia sets. By means of this method, the zero asymptotic sliding variables are applied to control the fractal identification. Furthermore, the problems of synchronization control are solved in the case of a drive system with unknown parameters, and the unknown parameters of the drive system can be identified in the asymptotic synchronization process. The results of simulation examples demonstrate the effectiveness of this new method. Particularly, the basic Julia set is also discussed.

Drive-Response Synchronization of a Fractional-Order Hyperchaotic System and Its Circuit Implementation

A novel fractional-order hyperchaotic system is proposed; the theoretical analysis and numerical simulation of this system are studied. Based on the stability theory of fractional calculus, we propose a novel drive-response synchronization scheme. In order to achieve this synchronization control, the Adams-Bashforth-Moulton algorithm is studied. And then, a drive-response synchronization controller is designed to realize the synchronization of the drive and response system, and the simulation results are given. At last, the fractional oscillator circuit of the new fractional-order hyperchaotic system is designed based on the EWB software, and it is verified that the simulation results of the fractional-order oscillator circuit are consistent with the numerical simulation results through circuit simulation.

Generalized projective lag synchronization between delay-coupled networks under circumstance noise

It is well known that time delay and random noise are universal in complex networks. However, the research on the synchronization of coupled networks that are subjected to delay-coupling and noise perturbation is very rare. In this paper, for two delay-coupled complex networks with different node dynamics, different topological structures and different numbers of nodes, under circumstance noise, the generalized projective lag synchronization between two networks is proposed for the first time. First, a more realistic theoretical framework is constructed for the drive-response network synchronization. Second, according to the LaSalle-type theorem for stochastic differential delay equations, we rigorously prove that the generalized projective lag synchronization between the drive-response networks can be achieved almost surely, by introducing an appropriate controller. Furthermore, numerical simulation is employed to verify the theoretical analysis. The results indicate that the drive-response networks can indeed achieve generalized projective lag synchronization, and that the synchronization is independent of time delay and scaling factor. Moreover, the remarkable influences of the update gain and the coupling delay on synchronization speed are revealed through the numerical results.

Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control

The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control.

Design an adaptive sliding mode controller for drive-response synchronization of two different uncertain fractional-order chaotic systems with fully unknown parameters

In this paper, design an adaptive sliding mode controller (ASMC) for master–slave synchronization of two different fractional-order chaotic systems with fully unknown parameters, uncertainties and external disturbances is proposed. The bounds of the unknown parameters, uncertainties and external disturbances are assumed to be unknown in advance. Appropriate adaptive laws are designed to tackle the unknown parameters, uncertainties and external disturbances. Based on the adaptive laws, the ASMC is constructed in order to ensure the occurrence of the sliding motion and synchronization of two different fractional-order systems. The analytical conditions for synchronization of the systems are obtained by utilizing Laplace transform. Finally, numerical examples are provided to illustrate the effectiveness of the proposed ASMC scheme.

Implementation of Chaos Synchronization on FPGA

Abstract A new method of achieving synchronization of chaotic systems on FPGA is proposed in this paper. We take Lorenz chaotic system as an example to simulate. The simulation is designed according to drive-response synchronization and master-slave synchronization, and implemented by using of the DSP Builder platform, which is part of Matlab/Simulink. The “*.mdl” files generated by DspBuilder are converted into “*.vhd” files by the use of the SignalComplie(a tool of DspBuilder). The timing simulation is finished in Quartus II, and finally implemented on FPGA. The results of the experiment show that the proposed method can work well on FPGA and the output signal is exhibited by oscilloscope.

Synchronization Criterion for Lur’e Systems via Delayed PD Controller

In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur’e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

Lag synchronization for fuzzy chaotic system based on fuzzy observer

A new fuzzy observer for lag synchronization is given in this paper. By investigating 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.

Design of fast state observers using a backstepping-like approach with application to synchronization of chaotic systems

A simple technique is introduced to build fast state observers for chaotic systems when only a scalar time series of the output is available. This technique relies on using a backstepping-like approach via introducing new virtual states that can be observed using the drive-response synchronization mechanism. The proposed dynamic structure of the virtual states allows for employing control parameters that can adjust the convergence rate of the observed states. In addition, these control parameters can be used to improve the transient performance of the response system to accommodate small and large variations of the initial conditions, thus achieving superior performance to conventional synchronization techniques. Simple Lyapunov functions are used to estimate the range of the control parameters that guarantees stable operation of the proposed technique. Three benchmark chaotic systems are considered for illustration; namely, the Lorenz, Chua, and Rossler systems. The conflict between stability and agility of the states observer is analyzed and a simple tuning mechanism is introduced. Implementation of the proposed technique in both analog and digital forms is also addressed and experimental results are reported ensuring feasibility and real-time applicability. Finally, advantages and limitations are discussed and a comparison with conventional synchronization methods is investigated.

Generalized projective synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

In this Letter, a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization” of a class of fractional-order chaotic systems via a scalar transmitted signal. This synchronization approach is theoretically and numerically studied. By using stability theory of linear fractional-order systems, the suitable conditions for achieving synchronization are given. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.

EXPONENTIAL SYNCHRONIZATION IN DRIVE-RESPONSE SYSTEMS OF HOPFIELD-TYPE NEURAL NETWORKS WITH TIME DELAYS

In this paper we investigate the drive-response type synchronization of Hopfield-type neural networks with connection time delays for both discrete and distributed cases. By employing the Lyapunov functional method, we propose a sufficient condition to ensure the occurrence of synchronization with exponential rates. This criterion is independent of time delays as well as the types of delay. We prove that the exponential synchronization occurs provided a certain weighted sum of the connection and coupling strengths is negative enough, no matter that the connection time delay is of discrete or distributed case. Numerical examples are provided to illustrate the results.

Application research on the chaos synchronization self-maintenance characteristic to secret communication

Chua’s circuit, which is improved to integrate conveniently, is presented. A drive-response chaotic synchronization system is constructed, which possesses a certain stability, resisting-disturbance, and so on. By means of research, it can be concluded that the chaotic synchronization system is provided with the characteristic of chaos synchronization self-maintenance. Utilizing the characteristic, the critical problem of how to simultaneously transmit the controlling signal of chaotic synchronization and the secret signal at a channel can be solved, and that a practical experiment validates the method; as a result, the research in the paper provides the foundation of putting chaos into practice application to secret communication.

Chaotic dynamics and synchronization of fractional-order Genesio–Tesi systems

In this paper, we investigate numerically the chaotic behaviours in the fractional-order Genesio–Tesi system. We find that chaos exists in the fractional-order Genesio–Tesi system with order less than 3. The lowest order we find to have chaos is 2.4 in this fractional-order Genesio–Tesi system. We propose a drive-response synchronization method for synchronizing the fractional-order chaotic Genesio–Tesi systems only using a scalar drive signal. This synchronization approach, based on stability theory of fractional-order systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal

Abstract In this paper, a drive-response synchronization method with linear output error feedback is presented for synchronizing a class of fractional-order chaotic systems via a scalar transmitted signal. Based on stability theory of fractional-order systems and linear system theory, a necessary and sufficient condition for the existence of the feedback gain vector such that global synchronization between the fractional-order drive system and response system can be achieved and its design method are given. This synchronization approach that is simple, global and theoretically rigorous enables synchronization of fractional-order chaotic systems be achieved in a systematic way and does not require the computation of the conditional Lyapunov exponents. An example is used to illustrate the effectiveness of the proposed synchronization method.

Two novel synchronization criterions for a unified chaotic system

Two novel synchronization criterions are proposed in this paper. It includes drive–response synchronization and adaptive synchronization schemes. Moreover, these synchronization criterions can be applied to a large class of chaotic systems and are very useful for secure communication.

Chaotic dynamics and synchronization of fractional-order Arneodo’s systems

Abstract In this paper, we numerically investigate the chaotic behaviors of the fractional-order Arneodo’s system. We find that chaos exists in the fractional-order Arneodo’s system with order less than 3. The lowest order we find to have chaos is 2.1 in this fractional-order Arneodo’s system. Our results are validated by the existence of a positive Lyapunov exponent. The linear and nonlinear drive–response synchronization methods are also presented for synchronizing the fractional-order chaotic Arneodo’s systems only using a scalar drive signal. The two approaches, based on stability theory of fractional-order systems, are simple and theoretically rigorous. They do not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization methods.