Characterisation of Multiple Patterns of Activity in Networks of Relaxation Oscillators with Inhibitory and Electrical Coupling

Authors:
Tiaza Bem;John Hallam
Affiliations:
Mærsk Mc-Kinney Møller Institute, University of Southern Denmark, Odense, and Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw,;Mærsk Mc-Kinney Møller Institute, University of Southern Denmark, Odense,
Venue:
IWINAC '09 Proceedings of the 3rd International Work-Conference on The Interplay Between Natural and Artificial Computation: Part I: Methods and Models in Artificial and Natural Computation. A Homage to Professor Mira's Scientific Legacy
Year:
2009

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Abstract

Fully-connected neural networks of non-linear half-center oscillators coupled both electrically and synaptically may exhibit a variety of modes of oscillation despite fixed topology and parameters. In suitable circumstances it is possible to switch between these modes in a controlled fashion. Previous work has investigated this phenomenon the simplest possible 2 cell network. In this paper we show that the 4 cell network, like the 2 cell, exhibits a variety of symmetrical and asymmetrical behaviours. In general, with increasing electrical coupling the number of possible behaviours is reduced until finally the only expressed behaviour becomes in-phase oscillation of all neurons. Our analysis enables us to predict general rules governing behaviour of more numerous networks, for instance types of co-existing activity patterns and a subspace of parameters where they emerge.