Fixed-time synchronization of fractional-order complex-valued neural networks with time-varying delay via sliding mode control

Abstract

Taking into account fractional-order complex-valued neural networks with time-varying delay, the issue of achieving fixed-time synchronization is discussed in this paper. By utilizing the properties of fractional calculus and fractional-order comparison principle, an improved lemma is proposed to derive the fixed-time synchronization conditions. On the basis of sliding model control and Lyapunov stability theorem, an effective sliding mode surface is constructed, which only uses the synchronization error information of FOCVNNs and is composed of fractional and integer integral terms. Further, a suitable sliding model control is constructed, which makes synchronization error converges to zero in a fixed-time. Beyond that, several sufficient conditions are posed to guarantee fixed-time synchronization of the fractional-order complex-valued neural networks and the upper bound of synchronization settling time is estimated. Finally, two numerical simulations are given to demonstrate the effectiveness of the presented theoretical results.