Projective-dual synchronization in delay dynamical systems with time-varying coupling delay

Abstract

The existence of projective-dual-anticipating, projective-dual, and projective-dual-lag synchronization in a coupled time-delayed systems with modulated delay time is investigated via nonlinear observer design approach. Transition from projectivedual-anticipating to projective-dual synchronization and from projective-dual to projective-dual-lag synchronization as a function of variable coupling delay τ p (t) is discussed. Using Krasovskii-Lyapunov stability theory, a general condition for projective-dual synchronization is derived. Numerical simulations on the chaotic Ikeda and Mackey-Glass systems are given to demonstrate the effectiveness of the theoretical results.

Finite-time Synchronization of Large-scale Hyper Chaotic Systems with Parametric Uncertainties and Time-varying Delay

“…It is concluded from the recent research that timedelayed system is still vulnerable for communication because the time delay τ can be exposed by several measures, such as filling factor 9 , autocorrelation 10 , one step prediction error 11 and so on. If the delay time τ is known, the time delayed system becomes quite a simple one, and the message encoded by the chaotic signal can be extracted by the common attack method 12 . Therefore, to realize the finite-time synchronization of chaotic systems with parametric uncertainties and time-varying delay, the aforementioned methods are no longer suitable, and a new analytical control scheme should be presented.…”

Dual synchronization of chaotic and hyperchaotic systems

“…Dual synchronization in modulated time delayed systems is discussed in [7]. Projective-dual synchronization in delay dynamical systems with time-varying coupling delay is investigated in [6]. Dual synchronization of chaotic and hyperchaotic systems with fully uncertain parameters via Adaptive control method is discussed in [14].…”

“…To the best of our knowledge, there are few theoretical results about dual synchronization of chaotic systems, and on the other hand, all of the aforementioned methods [6,7,13,15,18] are mainly concerned with the dual synchronization of chaotic systems with low dimensional attractors characterized by one positive Lyapunov exponent and do not consist of the dual synchronization of hyperchaotic systems. This feature limits the complexity of the chaotic dynamics.…”

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

“…It means these states are always in the first quadrant, such as the three species prey-predator systems [15,16,21], double Mackey-Glass systems [17,22,23], energy communication system in biological research [19,24], and virus-immune system [20]. For the three species preypredator systems, which consist of two competing preys and one predator can be described by the following set of nonlinear differential equations: = 1, 2 represent the densities of the two prey species and represents the density of the predator species.…”