Abstract:
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.
Keywords:neuron model, Hindmarsh – Rose system, chaos, hyperchaos, in-phase bursting