COEXISTENCE OF MULTISTABILITY AND CHAOS IN A RING OF DISCRETE NEURAL NETWORK WITH DELAYS

Abstract

A ring of discrete-time delayed neural network with self-feedback and a valid nonmonotonic activation function is explored. Coexistence of multiple stable equilibria and chaotic dynamics are demonstrated in this discrete dynamical system. Specifically, 2m stable stationary solutions and their basins of attraction are found for a loop with m-neurons network. The theory is established by formulating parameter conditions according to a geometric observation. The networks are further confirmed to exhibit chaotic dynamics when the magnitudes of inhibitory self-feedback weights are large enough. The scenario is based on building a snapback repeller and Marotto's theorem.