Abstract.
Oscillators in networks may display a variety of activity patterns. This paper presents a geometric singular perturbation analysis of clustering, or alternate firing of synchronized subgroups, among synaptically coupled oscillators. We consider oscillators in two types of networks: mutually coupled, with all-to-all inhibitory connections, and globally inhibitory, with one excitatory and one inhibitory population of oscillators, each of arbitrary size. Our analysis yields existence and stability conditions for clustered states, along with formulas for the periods of such firing patterns. By using two different approaches, we derive complementary conditions, the first set stated in terms of time lengths determined by intrinsic and synaptic properties of the oscillators and their coupling and the second set stated in terms of model parameters and phase space structures directly linked to parameters. These results suggest how biological components may interact to produce the spindle sleep rhythm in thalamocortical networks.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 9 September 1999 / Revised version: 7 July 2000 / Published online: 24 November 2000
Rights and permissions
About this article
Cite this article
Rubin, J., Terman, D. Analysis of clustered firing patterns in synaptically coupled networks of oscillators. J Math Biol 41, 513–545 (2000). https://doi.org/10.1007/s002850000065
Issue Date:
DOI: https://doi.org/10.1007/s002850000065