Nucleation in the FitzHugh-Nagumo system: Interface-spike solutions |
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Authors: | Xiaofeng Ren |
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Institution: | a Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA b Department of Mathematics, Chinese University of Hong Kong, Hong Kong, P.R. China |
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Abstract: | We find nucleation solutions of N interfaces and K spikes to the one-dimensional FitzhHugh-Nagumo system. Each spike sits asymptotically in the middle between two interfaces. We use the Lyapunov-Schmidt reduction method, in which the problem is split into a finite-dimensional problem related to the translation of the K spikes and an infinite-dimensional complement problem. However the complement problem remains near degenerate due to the translation of the N interfaces. To overcome this difficulty we move the interfaces by a small distance and solve the complement problem with the help of a Newton iteration argument. |
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Keywords: | Interface Spike Nucleation Lyapunov-Schmidt reduction Newton iteration |
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