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Asymptotic effects of boundary perturbations in excitable systems

A Neumann problem in the strip for the Fitzhugh Nagumo system is consid- ered. The transformation in a non linear integral equation permits to deduce a priori estimates for the solution. A complete asymptotic analysis shows that for large t the effects of the initial data vanish while the effects of bound- ary disturbances depend on the properties of the data. When they are convergent for large t, the solution is everywhere bounded; when theirs first derivatives belong to L one too, the effects are vanishing.

preprint2013arXivOpen access
M. De AngelisP. Renno
math-phmath.MPNeurons and Cognition
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M. De AngelisP. Renno

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