Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

Abstract

The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

A 4-Dimensional Discrete Chaotic System and Application in Image Encryption with Avalanche Effects

“…, (Y( ), X( ))) . (6) If there exists a transformation H : ℝ → ℝ (7) (X( )) = (ℎ 1 (X( )), ⋅ ⋅ ⋅ , ℎ (X( ))) (8) and a subset B = B X × B Y ⊂ ℝ × ℝ such that all trajectories of (1) and (2) with initial conditions in B satisfy…”

“…Since the earlier work of Pecora and Carroll [4], the research on GS has also developed rapidly ( [5], [6], [7], [8], [9], [10]). Moreover, GS may provide some new tools for cryptography and communications ( [11], [12], [13], [14], [15], [16], [17]).…”

A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

“…Therefore CGS has more general meaning than CS. The study of CGS has also attracted much attention (e.g., see [17][18][19][20][21][22][23][24][25]).…”

“…Since the pioneer work of Pecora and Carroll on CS secure communication [33], CS and CGS have been used as new tools in secure communications and have been used as designs of pseudorandom number generators (e.g., [17][18][19][20][21][22][23][24][25][34][35][36][37]). Research along this line is promising.…”

Linear and nonlinear generalized consensuses of multi-agent systems

“…On the other hand, in nonlinear science, the generalized synchronization [16][17][18][19][20][21][22] phenomena of chaotic systems have been intensively studied recently. In complete synchronization, the dynamics of two coupled systems totally coincide with each other; in generalized synchronization, a certain known or unknown functional relation exists between the dynamics of two coupled systems which are usually nonidentical.…”