Analysis of clustered firing patterns in synaptically coupled networks of oscillators |
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Authors: | Jonathan Rubin David Terman |
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Institution: | (1) Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, OH 43210, USA. e-mail: rubin@math.pitt.edu, US |
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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.
Received: 9 September 1999 / Revised version: 7 July 2000 / Published online: 24 November 2000 |
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Keywords: | : Oscillators – Clusters – Synaptic coupling – Geometric singular perturbation |
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