Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems

Abstract

The dynamics of two coupled neuron models, the Hindmarsh – Rose systems, are studied. Theirinteraction is simulated via a chemical coupling that is implemented with a sigmoid function.It is shown that the model may exhibit complex behavior: quasi-periodic, chaotic andhyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaosassociated with the appearance of a discrete Shilnikov attractor is described. It is shownthat the formation of these attractors leads to the appearance of in-phase burstingoscillations.