Multistability of discrete-time delayed Cohen–Grossberg neural networks with second-order synaptic connectivity.

This paper addresses the multistability problem of discrete-time delayed Cohen–Grossberg neural networks (DDCGNNs) with second-order synaptic connectivity. For the neural networks with nondecreasing saturated activation functions possessing 2 corner points, based on the partition space method and reduction ad absurdum, several sufficient conditions are derived to ensure that n -neuron second-order DDCGNNs can have 2 n locally exponentially stable equilibrium points. Then, the analyses are extended to nondecreasing saturated activation functions with 2 r corner points and some sufficient conditions are given to guarantee that the n -neuron DDCGNNs can have ( r + 1 ) n locally exponentially stable equilibrium points. Moreover, some conditions are obtained to ensure the existence of locally exponentially stable equilibrium point in a predesigned region. Finally, three examples are carried out to show the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]