Heteroclinic contours in oscillatory ensembles

Abstract

In this work, we study the onset of sequential activity in ensembles of neuronlike oscillators with inhibitorylike coupling between them. The winnerless competition (WLC) principle is a dynamical concept underlying sequential activity generation. According to the WLC principle, stable heteroclinic sequences in the phase space of a network model represent sequential metastable dynamics. We show that stable heteroclinic sequences and stable heteroclinic channels, connecting saddle limit cycles, can appear in oscillatory models of neural activity. We find the key bifurcations which lead to the occurrence of sequential activity as well as heteroclinic sequences and channels.