Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems

The dynamics of two coupled neuron models, the Hindmarsh – Rose systems, are studied. Their interaction 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 and hyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaos associated with the appearance of a discrete Shilnikov attractor is described. It is shown that the formation of these attractors leads to the appearance of in-phase bursting oscillations.