Periodic solutions of a one Dimensional Wilson-Cowan type model
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We analyze a time independent integral equation defined on a spatially extended domain which arises in the modeling of neuronal networks. In our survey, the coupling function is oscillatory and the firing rate is a smooth "heaviside-like" function. We will derive an associated fourth order ODE and establish that any bounded solution of the ODE is also a solution of the integral equation. We will then apply shooting arguments to prove that the ODE has two "1-bump" periodic solutions.
CitationKrisner, E. P. (2007). Periodic solutions of a one Dimensional Wilson-Cowan type model. Electronic Journal of Differential Equations, 2007(102), pp. 1-22.
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