Methods and Applications of Analysis

Volume 9 (2002)

Number 4

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

Pages: 493 – 516



M. Mimura

M. Nagayama

T. Ohta


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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