Monday 29 Oct 2012Persistent localised states in neural fields

Dr James Rankin - Neuromathcomp Project Team, INRIA Sophia-Antipolis, France

Harrison 103 15:00-16:00

The primary visual cortex (V1) has been shown to maintain localised
patterns of activity when oriented stimuli are presented in the visual
field (Chavane et al. 2011). We study these localised states with the
Wilson-Cowan-Amari neural field equations and take into account
features such as orientation preference in V1 in order to define a
biologically relevant spatial connectivity function. We find that for
a specific approximation of the connectivity function it is possible
to derive a PDE whose solutions correspond to steady states of the
full neural field equations. The PDE formulation allows for standard
dynamical systems tools to be applied in order to compute and path
follow both radially-symmetric bump solutions and
non-radially-symmetric patterns with D6 symmetry. Having identified
the types of solution produced in different regions of parameter
space, the next step is to introduce an input. In this case, the PDE
approximation is no longer valid and we study the dynamics of the full
equations using an implementation on GPU architecture. Finally, the
implications of our results are discussed with respect to experimental
findings.

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