Projective Lag Synchronization Research Articles

Linear observer based projective synchronization in delay Rössler system

Abstract A new type of linear observer based projective, projective anticipating and projective lag synchronization of time-delayed Rossler system is studied. Along with this, the approach arbitrarily scales a drive system attractor and hence a similar chaotic attractor of any desired scale can be realized with the help of a synchronizing scaling factor. A scalar synchronizing output is considered where the output equation includes both the delay and non-delay terms of the nonlinear function. The condition for synchronization is derived analytically and the values of the coupling parameters are obtained. Analytical results are verified through numerical investigation and the effect of modulated time delay in the method is discussed. An important aspect of this method is that it does not require the computation of conditional Lyapunov exponents for the verification of synchronization.

Increasing-order Projective Synchronization of Chaotic Systems with Time Delay

This work is concerned with lag projective synchronization of chaotic systems with increasing order. The systems under consideration have unknown parameters and different structures. Combining the adaptive control method and feedback control technique, we design a suitable controller and parameter update law to achieve lag synchronization of chaotic systems with increasing order. The result is rigorously proved by the Lyapunov stability theorem. Moreover, corresponding simulation results are given to verify the effectiveness of the proposed methods.

Global Exponential Projective Synchronization and Lag Synchronization of Hyperchaotic Lü System

This paper investigates the projective synchronization and lag synchronization of a new hyperchaotic system [Physica A 364 (2006) 103]. On the basis of Lyapunov stability theory, two novel nonlinear controllers are respectively designed to guarantee the global exponential projective synchronization (including complete synchronization and anti-synchronization) and lag synchronization. Finally, numerical simulations are given to show the effectiveness of the main results.

Generalized projective synchronization in time-delayed systems: Nonlinear observer approach

In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable synchronization (anticipatory and lag) for a large class of time-delayed systems in which the response system's trajectory is forced to have an amplitude proportional to the drive system. The constant of proportionality is determined by the control law, not by the initial conditions. The proposed technique has been applied to synchronize Ikeda and prototype models by numerical simulation.

Projective lag synchronization in chaotic systems

In this paper, a new projective lag synchronization is proposed, where a driven chaotic system synchronizes the past state of the driver up to a scaling factor α . An active control method is employed to design a controller to achieve the global synchronization of two identical chaotic systems. Based on Lyapunov stability theorem, a sufficient condition is then given for the asymptotical stability of the null solution of an error dynamics. The effectiveness of the proposed schemes is verified via numerical simulations.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey–Glass systems on Erdös–Rényi networks.

Projective-Lag Synchronization of Coupled Multidelay Feedback Systems

In this study, we investigate the projective-lag synchronization model of coupled multidelay feedback systems. The master synchronizes with the slave under the lag synchronization scheme and there is a scale factor between the amplitudes of state variables. The driving signal is constituted by the sum of multiple nonlinear transformations of a delayed state variable. A sufficient condition for synchronization is considered under the Krasovskii–Lyapunov theory. The effectiveness of the proposed model is demonstrated and verified by examining specific examples using modified Mackey-Glass and Ikeda systems.