Coexistence and local stability of multiple equilibria in competitive neural networks with nondecreasing activation functions

In this paper, the multistability is discussed for competitive neural networks (CNNs) with nondecreasing saturated activation functions with 2 r corner points. Based on decomposition of state space, Cauchy convergence principle and inequality technique, some sufficient conditions ensuring the local exponential stability of (r + 1)^N equilibrium points are derived. The obtained results are less restrictive than some recent works. An example with simulation is presented to verify the theoretical analysis.