Projective synchronization of time‒delayed chaotic systems with unknown parameters using adaptive control method

Abstract

The present article aims to study the projective synchronization between two identical and non‒identical time‒delayed chaotic systems with fully unknown parameters. Here the asymptotical and global synchronization are achieved by means of adaptive control approach based on Lyapunov–Krasovskii functional theory. The proposed technique is successfully applied to investigate the projective synchronization for the pairs of time‒delayed chaotic systems amongst advanced Lorenz system as drive system with multiple delay Rössler system and time‒delayed Chua's oscillator as response system. An adaptive controller and parameter update laws for unknown parameters are designed so that the drive system is controlled to be the response system. Numerical simulation results, depicted graphically, are carried out using Runge–Kutta Method for delay‒differential equations, showing that the design of controller and the adaptive parameter laws are very effective and reliable and can be applied for synchronization of time‒delayed chaotic systems. Copyright © 2014 John Wiley & Sons, Ltd.