A New Generalized-Type of Synchronization for Discrete-Time Chaotic Dynamical Systems

Abstract

In this paper, a new type of chaos synchronization in discrete-time is proposed by combining matrix projective synchronization (MPS) and generalized synchronization (GS). This new chaos synchronization type allows us to study synchronization between different dimensional discrete-time chaotic systems in different dimensions. Based on nonlinear controllers and Lyapunov stability theory, effective control schemes are introduced and new synchronization criterions are derived. Numerical simulations are used to validate the theoretical results and to verify the effectiveness of the proposed schemes.

Chaos, control, and synchronization in some fractional-order difference equations

“…The following theorem presents the control laws to stabilize the fractional Wang map (28). The proof has been omitted as it follows the same lines of Theorems 3 and 4.…”

“…In Fig. 19, we show the bifurcation diagram of the fractional Wang map (28) with υ ∈ [0.9, 1] as the critical parameter. We see that the map exhibits a chaotic behavior over a short interval of fractional orders.…”

“…This was the seed that started the long use of chaotic systems in the field of communications. Throughout the years, many studies have considered the synchronization of integer-order chaotic and hyperchaotic maps including [25][26][27][28][29] but very few can be found for those of fractional-order [30][31][32][33][34].…”

On Matrix Projective Synchronization and Inverse Matrix Projective Synchronization for Different and Identical Dimensional Discrete-Time Chaotic Systems

“…In this example, the synchronization criterion presented in Section 3 is applied between systems (18) and (19). Then, quantities and ( ( )) are given by, respectively, = ( 1 0 0 ) , ( ( )) = ( 0…”

“…Many powerful methods have been reported to investigate some types of chaos (hyperchaotic) synchronization [5][6][7][8][9][10] and most of works on synchronization have been concentrated on continuous-time chaotic systems rather than discrete-time chaotic systems. Recently, more attention has been paid to the synchronization of chaos (hyperchaos) in discrete-time dynamical systems [11][12][13][14][15][16][17][18][19], due to its applications in secure communication and cryptology [20][21][22].…”