Projective Synchronization of Uncertain Chaotic Systems with Different Dimensions and External Noise Disturbance

This work aims to synchronize uncertain chaotic systems with noise disturbance by means of an adaptive active nonlinear control approach. Since the dimensions of the synchronizing chaotic systems considered are not the same. So, the increased order projective synchronization is employed on the given chaotic systems. A general control law, noise estimation, and system parameter updating law are proposed for synchronizing the uncertain master and slave systems with noise disturbance. Furthermore, the 3
^rd
order Lu chaotic system and 4
^th
order Rossler hyperchaotic system serve as illustrations for the mathematical analysis of the proposed approach. The states of the two synchronizing systems will synchronize up to a proportional scale. To verify the asymptotic stability of error dynamics of synchronizing systems, Lyapunov stability criteria is used. To investigate the validity of the proposed approach, mathematical simulations are presented graphically.