Methods and Applications of Analysis

Non-annihilation of Travelling Pulses in a Reaction-diffusion System

M. Mimura, M. Nagayama, and T. Ohta

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It is demonstrated that slowly travelling pulses arising in a reaction-diffusion (RD) system with the FitzHugh-Nagumo type nonlinearity do not necessarily annihilate but reflect off of each other before they collide. This phenomenon is in contrast with the well-known annihilation of travelling pulses on nerve axon and expanding rings in the Belousov-Zhabotinsky chemical reaction. By using singular perturbation methods, we derive a fourth order system of ODEs from the RD system, and study non-annihilation phenomenon of very slowly travelling pulses.

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Methods Appl. Anal., Volume 9, Number 4 (2002), 493-516.

First available in Project Euclid: 1 September 2009

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Mimura, M.; Nagayama, M.; Ohta, T. Non-annihilation of Travelling Pulses in a Reaction-diffusion System. Methods Appl. Anal. 9 (2002), no. 4, 493--516.

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