Synchronization for fractional-order discrete-time neural networks with time delays

Abstract

This paper is concerned with synchronization for fractional-order discrete-time neural networks (FDTNNs) without time delays and with time delays, respectively. First of all, the inequality on Riemann-Liouville fractional difference is proved in the light of the feather of the discrete function A(ν)(k), 0 < ν ≤ 1, which plays an important role in the investigation of the synchronization. Under the feedback controllers, synchronization conditions of FDTNNs without time delays and with time delays are derived by means of different techniques. Based on the inequality and the comparison principle of linear fractional difference system, the synchronization condition of FDTNNs without time delays is obtained. Further more, the synchronization condition of FDTNNs with time delays is derived through Lyapunov direct method with a suitable Lyapunov function involving discrete fractional sum term, which depends on the definition of Riemann-Liouville fractional difference. Lastly, simulations of two examples are provided to prove the effectiveness of the approaches.