Synchronization Of Non-identical Chaotic Systems Research Articles

Design of an Analog Time-Varying Audio Cryptography System Based on Sliding Mode Synchronization of Non-identical Chaotic Systems Described with Time-Delayed Fractional-Order Dynamics

Design of an Analog Time-Varying Audio Cryptography System Based on Sliding Mode Synchronization of Non-identical Chaotic Systems Described with Time-Delayed Fractional-Order Dynamics

Control and stability on chaotic convection in porous media with time delayed fractional orders

In this paper, we study the effect of time delay and the scaled Rayleigh number on chaotic convection in porous media with fractional order. The stability analysis for different fractional-order cases is investigated and the effective chaotic range of the fractional order is determined by a general synchronization of nonidentical chaotic systems based on the active control technique. The numerical results demonstrate that the effect of various values of the scaled Rayleigh number R, time delay and fractional orders changes the chaotic convection behavior to limit cycles or stable system in porous media.

Finite-time synchronization of nonidentical chaotic systems with multiple time-varying delays and bounded perturbations

This paper is concerned with synchronization in a setting time for drive-response chaotic systems with multiple time-varying delays. The driving and response systems exhibit different dynamical behaviors with nonidentical delays and uncertain bounded external perturbations. Due to the time delays, existing finite-time stability theorem cannot be applied to the synchronization goal. By designing suitable controller and designing some Lyapunov–Krasovskii functionals, sufficient conditions guaranteeing the finite-time synchronization are derived without using existing finite-time stability theorem. Results of this paper extend most of existing ones which can only finite-timely synchronize coupled identical systems without delay. Numerical simulations demonstrate the effectiveness of the theoretical analysis.

A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty

In this paper, a class of integer and fractional-order chaotic systems, which undergoes external disturbances and system uncertainties, are considered. A robust synchronization scheme that incorporates a sliding mode controller established on a new fractional-order surface. A fractional order derivative provides an additional degree of freedom in the sliding surface. After that, the stability analysis for closed loop system is studied. Then, based on a Lyapunov function candidate an adaptive switching gain is derived which make the controller capable to bring the synchronizing error to zero without any disturbance exerted upon the stability. The proposed method is designed for a wide class of chaotic systems. Furthermore, the results are extended for fractional-order version of chaotic systems. The proposed controller can be used to both integer and fractional order chaotic systems. The design is simple with rigorous stability analysis. Several numerical simulations are provided to verify the effectiveness of the theoretical results.

Non-Identical Synchronization, Anti-Synchronization and Control of Single-Machine Infinite-Bus Power System via Active Control

Since the idea of synchronizing two identical chaotic systems under different initial conditions was first introduced by Pecora and Carroll, the synchronization of chaotic systems has attracted much attention, and the synchronization of non-identical chaotic systems has also been investigated. Single-Machine Infinite-Bus (SMIB) power system has nonlinear behaviour. On account of avoiding undesirable behaviours in power systems such as voltage collapse, the synchronization and control of SMIB power system have considerable importance. This paper presents chaos synchronization and anti-synchronization of SMIB power system to Duffing oscillator by means of active control method. The sum of synchronization and anti-synchronization signals converge asymptotically to zero and achieve the control of SMIB power system. Numerical simulations are used to demonstrate the validity of proposed active control method on the non-identical synchronization, anti-synchronization and control of SMIB power system. DOI: http://dx.doi.org/10.5755/j01.itc.43.2.4677

Adaptive function Q‐S synchronization of chaotic systems with unknown parameters

AbstractThis work investigates the adaptive function Q‐S synchronization of non‐identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q‐S synchronization with a desired scaling function of two different chaotic systems (including different dimensional systems) are derived based on the Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the Q‐S synchronization of non‐identical chaotic systems is to be achieved. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme. Copyright © 2009 John Wiley & Sons, Ltd.

A general scheme for Q–S synchronization of chaotic systems with unknown parameters and scaling functions

This work investigates Q–S synchronization of non-identical chaotic systems with unknown parameters and scaling function. The sufficient conditions for achieving Q–S synchronization with a double-desired scaling function of two different chaotic systems (including different dimensional systems) are derived based on the Lyapunov stability theory. By the adaptive control technique, the corresponding parameter update laws are proposed such that the Q–S synchronization of non-identical chaotic systems is to be obtained. Two illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

Adaptive Q–S synchronization of non-identical chaotic systems with unknown parameters

This work investigates the adaptive Q–S synchronization of non-identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q–S synchronization of two different chaotic systems (including different dimensional systems) are derived, based on Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the non-identical chaotic systems are to have Q–S synchronization. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.

Minimization of the energy flow in the synchronization of nonidentical chaotic systems

We argue that maintaining a synchronized regime between different chaotic systems requires a net flow of energy between the guided system and an external energy source. This energy flow can be spontaneously reduced if the systems are flexible enough as to structurally approach each other through an adequate adaptive change in their parameter values. We infer that this reduction of energy can play a role in the synchronization of bursting neurons and other natural oscillators.

An adaptive fuzzy observer-based approach for chaotic synchronization

This paper presents an adaptive fuzzy observer design to synchronize chaotic systems. The chaotic system is expressed in the form of Takagi–Sugeno fuzzy model (T–S fuzzy system), which considers the effect of model mismatches. Based on this model, an adaptive fuzzy observer is developed to deal with the synchronization of nonidentical chaotic systems. In contrast to the framework of parallel distributed compensation for T–S fuzzy system, the proposed method does not rely on the existence of common matrix P which is imposed in stability conditions. The computer simulation examines the performance of two well-known chaotic systems, Lorenz system and Chua circuit. The results show that the proposed approach cannot only attain synchronization but also is robust to parameter perturbations in the drive system.