In this paper, we propose a new approach of designing a controller and an update rule of unknown parameters for synchronizing fractional-order system with multiple delays and prove the correctness of the approach according to the fractional Lyapunov stable theorem. Based on the proposed approach, synchronizing fractional delayed chaotic system with and without unknown parameters is realized. Numerical simulations are carried out to confirm the effectiveness of the approach.

This paper is concerned with synchronization of two coupled Hind-marsh-Rose (HR) neurons. Two synchronization criteria are derived by using nonlinear feedback control and linear feedback control, respectively. A synchronization criterion for FitzHugh-Nagumo (FHN) neurons is derived as the application of control method of this paper. Compared with some existing synchronization results for chaotic systems, the contribution of this paper is that feedback gains are only dependent on system parameters,...