Adaptive reduced-order modified function projective synchronization of chaotic systems with uncertain parameters

This letter deals with the modified function projective synchronization of chaotic systems with different orders and uncertain parameters. The problem of synchronization of chaotic systems with different orders is translated into the synchronization of chaotic systems with same orders by using reduced-order method. Based on adaptive control and Lyapunov stability theory, the nonlinear controller with corresponding update laws are designed such that the two chaotic systems with different orders can be reduced-order modified function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.