Generalized projective lag synchronization between different hyperchaotic systems with uncertain parameters

Abstract

Generalized projective lag synchronization (GPLS) is characterized by the output of the drive system proportionally lagging behind the output of the response system. In this paper, GPLS between different hyperchaotic systems with uncertain parameters, i.e., GPLS between Lorenz and Lü hyperchaotic systems, and between Lorenz-Stenflo and Lorenz hyperchaotic systems, is studied by applying an adaptive control method. Based on Lyapunov stability theory, the adaptive controllers and corresponding parameter update rules are constructed to make the states of two diverse hyperchaotic systems asymptotically synchronize up to the desired scaling matrix and to estimate the uncertain parameters. Some numerical simulations are provided to show the effectiveness of our results.

Shape Synchronization in Driver-Response of 4-D Chaotic System and Its Application in Image Encryption

“…Various concepts of chaotic synchronization have been proposed, such as complete synchronization [61], [62], lag synchronization [63], projective synchronization [64], [65], phase synchronization [66], partial synchronization [67], general synchronization [68], anti-synchronization [69], [70]. These concepts of chaotic synchronization almost focus on state variables of drive and response systems.…”

Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure

“…During the past three decades, chaos synchronization has been a hot topic in nonlinear science due to its various applications [1][2][3]. A variety of synchronization approaches have been revealed, such as complete synchronization (CS) [4], antisynchronization (AS) [5], phase synchronization [6], lag synchronization (LS) [7], projective synchronization (PS) [8], function projective synchronization (FPS) [9][10][11], and others [12,13]. Recently, modified function projective synchronization (MFPS) is proposed, in which the drive system and the response system could be synchronized up to a scaling function matrix [14].…”