Seminar series
Date
Thu, 02 Mar 2006
16:30
16:30
Location
DH 1st floor SR
Speaker
Stephen Coombes
Organisation
Nottingham
I will discuss the dynamics of
synaptically coupled model neurons that undergo a form of accommodation in the
presence of sustained activity. The basic model is an integral equation for
synaptic activity that depends upon the non-local network connectivity, synaptic
response, and firing rate of a single neuron. A phenomenological model of
accommodation is examined whereby the firing rate is taken to be a simple
state-dependent threshold function. As in the case without threshold
accommodation classical Mexican-Hat connectivity is shown to allow for the
existence of spatially localised states (bumps). Importantly an analysis of bump
stability (in both one and two spatial dimensions) using recent Evans function
techniques shows that bumps may undergo instabilities leading to the emergence
of both breathers and travelling waves. Numerical simulations show that
bifurcations in this model have the same generic properties as those seen in
many other dissipative systems that support localised structures, and in
particular those of coupled cubic complex Ginzburg-Landau equations, and three
component reaction diffusion equations. Interestingly, travelling pulses in this
model truly have a discrete character in the sense that they scatter as auto-solitons.
/notices/events/abstracts/differential-equations/ht06/Coombes.shtml