Applying the 0-1 Test for the Detection of Chaotic and Reduced-order Synchronization of Chaotic Systems with Different Dimension

Abstract

In this paper, we are applying the 0-1 test for detection of chaotic of dynamical systems. Also, my purpose is synchronization of the chaotic systems with an arbitrary different order system, by applying an appropriate control signal, so that it follow behavior a chaotic system that parameters are unknown. The main feature of the reduced-order synchronization is that the order of the slave system is less than the master system. A widely variety of approaches have been proposed for chaos synchronization, such as: adaptive control, linear and nonlinear feedback control, active control.

In this paper, we after detection chaos of two chen and lu systems applying of the 0-1 test , synchronize they by the reduced-order method. Also, by choosing appropriate positive definite Lyapunov function, the stability of the system were investigated for the various parameters. The advantage of this controller design is the time variable its coefficients.