Metastable states and transient activity in ensembles of excitatory and inhibitory elements

¹ Department of Control Theory, Nizhny Novgorod University - Gagarin Avenue, 23, 603950 Nizhny Novgorod,  Russia
² K.U. Leuven, ESAT-SCD/SISTA - Kasteelpark Arenberg 10, B-3001 Leuven (Heverlee), Belgium, EU

^a makomar@mail.ru

Received: 20 May 2010
Accepted: 12 July 2010

Abstract

Complex activity in biological neuronal networks can be represented as a sequential transition between complicated metastable states. From a dynamical systems theory point of view sequential activity in neuronal networks is associated with the existence of stable heteroclinic contours in the phase space of the corresponding neuronal model. Previously, the conditions of existence and stability of these contours have been studied in networks consisting of only inhibitory synaptically coupled cells. In this paper the effect of excitatory neurons is studied. In contrast to early studied cases, in the considered model the heteroclinic trajectories are located on two-dimensional manifolds. This leads to the existence of an infinitely large number of transitions between metastable states. The conditions for the existence of metastable states and arising sequential dynamics are presented.