heteroclinic contour

Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator.

Recent experimental and theoretical studies indicate that slow brain rhythms are generated by simple inhibitory neural networks. Sequential switching of tonic spiking activity is a widespread phenomenon underlying such rhythms. In this paper, we analyze a minimal, reciprocally connected circuit of three spiking units in the cases of different excitability classes of models. It is shown that in both types arising of stable heteroclic contour produces sequentail activation and slow rhythm generation in neural microcircuit. Bifurcation of heteroclinic contour arising is investigated.

Switching activity in the ensemble of inhibitory coupled Poicare systems is considered. The existence of heteroclinic contour in the phase space at the certain domain of parameter space has shown.

Dynamics of the ensemble of non-identical inhibitory and diffusively coupled systems of Poincare is considered. The approximate bifurcation diagrams for all qualitatively different regimes of the network activity have shown. There are areas of the parameter space corresponding to different dynamic regimes, such as multistability, extinction, modulation, bursting and synchronization.