Neuronal multistability induced by delay

Abstract

Feedback circuits are important for understanding the emergence of patterns of neural activity. In this contribution we study how a delayed circuit representing a recurrent synaptic connection interferes with neuronal nonlinear dynamics. The neuron is modeled using a Hodgkin-Huxley type model in which the firing pattern depends on subthreshold oscillations, and the feedback is included as a time delayed linear term in the membrane voltage equation. In the regime of sub-threshold oscillations the feedback amplifies the oscillation amplitude, inducing threshold crossings and firing activity that is self regularized by the delay. We also study a small neuron ensemble globally coupled through the delayed mean field. We find that the firing pattern is controlled by the delay. Depending on the delay, either all neurons fire spikes, or they all exhibit subthreshold activity, or the ensemble divides into clusters, with some neurons displaying subthreshold activity while others fire spikes. © Springer-Verlag Berlin Heidelberg 2007.