Aτ-type stability criteria in division regions for multitime-scale networks with delays

Abstract

This paper is concerned with new results on A -type stability criteria in division regions for competitive neural networks with different time scales. Under the decomposition of state space, both the neural activity levels (the short-term memory) and the synaptic modifications (the long-term memory), are taken into account in constructing division regions that allow the coexistence of equilibrium points. Meanwhile, novel delay-dependent multistability and monostability criteria are established in division regions that depend on divisions in index set of neurons and boundedness of unsupervised synaptic variables. The attained results show the effects of self-interactions of neurons and Hebbian learning behavior on the multistable convergence of the networks. Finally, numerical simulations will illustrate multistable neuron activity and synaptic dynamics of multitime-scale competitive networks.