Synchronization of Different Dimensions Fractional-Order Chaotic Systems with Uncertain Parameters and Secure Communication

In this paper, an adaptive modified function projective synchronization (AMFPS) scheme of different dimensions fractional-order chaotic systems with fully unknown parameters is presented. On the basis of fractional Lyapunov stability theory and adaptive control law, a new fractional-order controller and suitable update rules for unknown parameters are designed to realize the AMFPS of different fractional-order chaotic systems with non-identical orders and different dimensions. Theoretical analysis and numerical simulations are given to verify the validity of the proposed method. Additionally, synchronization results are applied to secure communication via modified masking method. Due to the unpredictability of the scale function matrix and using of fractional-order systems with different dimensions and unequal orders, the proposed scheme has higher security. The security analysis demonstrate that the proposed algorithm has a large key space and high sensitivity to encryption keys and it is resistance to all kind of attacks.