Multiple [formula omitted] stability and instability of time-varying delayed fractional-order Cohen-Grossberg neural networks with Gaussian activation functions

Abstract

This paper formulates new theoretical results concerning the multiple O(t-q) stability and instability for a class of time-varying delayed fractional-order Cohen-Grossberg neural networks (FoCGNNs) with Gaussian activation functions. With the aid of geometrical configurations obtained from the FoCGNNs model and Gaussian functions, the state space are partitioned into 3k subspaces, where k is a nonnegative constant determined by the parameters of FoCGNNs model. By means of the Brouwer’s fixed point theorem as well as the contraction mapping, it is guaranteed that there exists a unique equilibrium point in each subspace. Sufficient conditions are achieved that 2k equilibrium points are locally O(t-q) stable and 3k-2k equilibrium points are unstable. Several examples are rendered to demonstrate the feasible analysis of the theoretical results.