Projective synchronization of different uncertain fractional-order multiple chaotic systems with input nonlinearity via adaptive sliding mode control

This paper introduces the projective synchronization of different fractional-order multiple chaotic systems with uncertainties, disturbances, unknown parameters, and input nonlinearities. A fractional adaptive sliding surface is suggested to guarantee that more slave systems synchronize with one master system. First, an adaptive sliding mode controller is proposed for the synchronization of fractional-order multiple chaotic systems with unknown parameters and disturbances. Then, the synchronization of fractional-order multiple chaotic systems in the presence of uncertainties and input nonlinearity is obtained. The developed method can be used for many of fractional-order multiple chaotic systems. The bounds of the uncertainties and disturbances are unknown. Suitable adaptive rules are established to overcome the unknown parameters. Based on the fractional Lyapunov theorem, the stability of the suggested technique is proved. Finally, the simulation results demonstrate the feasibility and robustness of our suggested scheme.

A New Type of Combination Synchronization among Multiple Chaotic Systems

Based on former combination synchronization studies, a new type of combination synchronization approach is developed in this research, with the consideration of parallel combination of drive systems. This new synchronization approach is referred to as combination synchronization-II. As a representative case, the combination synchronization-II between three drive systems and one response system is studied. Applying Lyapunov stability theorem and active backstepping design, sufficient conditions for the proposed combination synchronization approach are derived. Numerical simulations are performed to show the feasibility and effectiveness of the proposed approach. Based on the investigation in this research, the proposed approach provides an applicable method for designing universal combination synchronization among multiple chaotic systems.