Synchronization in time-discrete model of two electrically coupled spike-bursting neurons

Dynamics of the ensemble of two model neurons interacting through electrical synapse is investigated. Both neurons are described by two-dimensional discontinuous map. It is shown that in four-dimensional phase space a chaotic attractor of relaxation type exists corresponding to spike-bursting chaotic oscillations. A new effect of recurrent transitory chaotic oscillations underlies a dynamical mechanism of chaotic bursts formation. It is shown that, under coupling, the transient from chaotic bursts generation into rest state occurs with a time delay. A new characteristic estimating the degree of spike-bursting synchronization is introduced. Dependence of the synchronism degree on the coupling strength is shown for some coupling interval where only activity synchronization occurs. A probabilistic study provides a dynamical explanation of these phenomena.

► The chaotic attractor of relaxational type exists in the system corresponding to chaotic spiking-bursting oscillations of neurons.
► A new effect of recurrent transitory chaotic oscillation underlies a dynamical mechanism of chaotic bursts formation.
► A new characteristic estimating the degree of spike-bursting synchronization is introduced.
► For some coupling interval the bursting activity synchronization occurs.