Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations

Abstract

This article, we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous neuron activation functions (FCGNNDDs). First, under the framework of Filippov theory and differ- ential inclusion theoretical analysis, the global existence of Filippov solution for FCGNNDDs is studied by means of the given growth condition. Second, by virtue of suitable Lyapunov functional, Young inequality and comparison theorem for fractional order delayed linear system, some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations. Third, the global asymptotic synchronization condition for FCGNNDDs is obtained based on the pinning control. At last, two numerical simula- tions are given to verify the theoretical findings.