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| The goal of this work is to study how long-range connections in the primary visual cortex of mammals can influence local cortical activity as seen in optical imaging experiments. It is known that the perception of contours in the primary visual cortex is locally organized around "pinwheels" and possess an approximate Euclidean invariance when only local connections are considered. Moreover recent experimental evidences support that the local circuitry operates at the edge of an instability where the network shows self-sustained stationary/oscillatory activity.
Assuming (to simplify the analysis) that the pinwheels are organized in a square lattice, we consider the effects of long-range (non local) connections as modeled in Bressloff:03. It produces a forced symmetry-breaking in the equations which, as we have shown, can lead to oscillatory and/or intermittent dynamics around the static square pattern produced by the local connections. This dynamics is closely related to the occurrence of heteroclinic cycles for the system.
The tools are equivariant dynamical systems theory and degree theory. Numerical experiments support the theoretical analysis. |
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