Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems

Abstract

This work investigates modified function projective synchronization between two different hyperchaotic dynamical systems, namely, hyperchaotic Lorenz system and hyperchaotic Chen system with fully unknown parameters. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between two diffierent hyperchaotic dynamical systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

DYNAMICAL BEHAVIORS OF A NEW HYPERCHAOTIC SYSTEM WITH ONE NONLINEAR TERM Vol. 3(1) Jan 2015, No. 1, pp. 1-18 A.M.A. EL-SAYED, H.M. NOUR, A. ELSAID, A. ELSONBATY

“…The existence and uniqueness of the solution is studied in the region J where J = (0; T ] and = f(x; y; z; w) : maxfjxj ; jyj ; jzj ; and jwjg Ag: (10) The solution of ( 5) and ( 6) is given by:…”

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

“…Zheng [22] investigated the MFPS between two different dimensional chaotic systems with fully unknown or partially unknown parameters via increased order method, designed a unified adaptive controller and parameter update laws, and the control strength of the controller can adaptively be identified. Reference [23] studied the MFPS between fourdimensional Lorenz and Chen hyperchaotic dynamical systems with fully unknown parameters; scaling function matrix had the form of Mℎ( ), M is a constant diagonal matrix and ℎ( ) is a continuous differentiable function with ℎ( ) ̸ = 0, and the scaling function matrix is more flexible and variable through choosing different M and ℎ( ). So, it has broad application prospects in practical situations [24].…”