# American Institute of Mathematical Sciences

September  2014, 19(7): 2039-2045. doi: 10.3934/dcdsb.2014.19.2039

## Asymptotic effects of boundary perturbations in excitable systems

 1 University of Naples Federico II, Via Claudio, 21, Naples, 80121, Italy, Italy

Received  April 2013 Revised  March 2014 Published  August 2014

A Neumann problem in the strip for the Fitzhugh Nagumo system is considered. 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 boundary disturbances $\varphi_1 (t),$ $\varphi_2(t)$ depend on the properties of the data. When $\varphi_1,\,\, \varphi_2$ are convergent for large $t$, the solution is everywhere bounded and depends on the asymptotic values of $\varphi_1 ,$ $\varphi_2$. More, when $\varphi_i \in L^1 (0,\infty) (i=1,2)$ too, the effects are vanishing.
Citation: Monica De Angelis, Pasquale Renno. Asymptotic effects of boundary perturbations in excitable systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2039-2045. doi: 10.3934/dcdsb.2014.19.2039
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