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Stephen Coombes

School of Mathematical Sciences, Nottingham University, UK


Wednesday 27 May 2009


Seminar Room B10 (Basement)

Alexandra House, 17 Queen Square, London, WC1N 3AR


Dynamics of Morris-Lecar networks

The Morris-Lecar (ML) neuron model is a two dimensional conductance based model that is often used as an idealised fast-spiking pyramidal neuron.  Its planar nature has encouraged much analysis of the single neuron model using tools from phase-plane analysis and the "geometry of excitability".  When treating synaptic or gap junction coupled networks of oscillating ML neurons these techniques are the natural basis for developing a weakly-coupled oscillator theory.  However, to probe network dynamics in the strong coupling regime requires an alternative approach.  I will show how results in this area can be obtained by using a piece-wise linear caricature of the ML model.  In illustration of the usefulness of such an approach I will first consider gap junction coupling and show how to analyse emergent fluctuations in the mean membrane potential (as instabilities of an asynchronous network state).  Next I will treat synaptically coupled networks with a phenomenological form of retrograde second messenger signalling that can support depolarisation induced suppression of excitation.  In this case I will describe a mechanism for the emergence of ultra-low frequency synchronised oscillations.