Pattern Formation in a Network of Excitatory and Inhibitory Cells with Adaptation

A bifurcation analysis of a simplified model for excitatory and inhibitory dynamics is presented. Excitatory cells are endowed with a slow negative feedback and inhibitory cells are assumed to act instantly. This results in a generalization of the Hansel-Sompolinsky model for orientation selectiv- ity. Normal forms are computed for the Turing-Hopf instability, where a new class of solutions is found. The transition from stationary patterns to traveling waves is analyzed by deriving the normal form for a Takens-Bogdanov bifurcation. Comparisons between the normal forms and numerical solutions of the full model are presented.

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