Direct approach on fixed-time stabilization and projective synchronization of inertial neural networks with mixed delays

Abstract

This article mainly addresses the problems of fixed-time stabilization(FTS) and fixed-time projective synchronization(FTPS) for the chaotic inertial neural networks(INNs) with mixed delays. Unlike the previous works, the results of FTS and FTPS are constructed for the chaotic INNs by means of direct approach instead of reduced-order way, which are more intuitive and concise. Furthermore, by designing effective Lyapunov functionals and novel feedback controllers, we obtain sufficient condition to respectively ensure FTS and FTPS of the delayed chaotic INNs, which settling times of FTS and FTPS do not depend on any initial values of the investigated systems. Until now, very few works are reported on FTS and FTPS for the delayed chaotic INNs via non-reduced-order way. In addition, the proposed FTPS are more generalized than the conventional synchronization and anti-synchronization. At last, some simulation results and applications are listed to expound the correctness of the derived criteria.