On propagation failure in 1 and 2 dimensional excitable media

Details On propagation failure in 1 and 2 dimensional excitable media On propagation failure in 1 and 2 dimensional excitable media

2004-08-17

arxiv.org/abs/nlin/0408026v1

Nonlinear Sciences

Pattern Formation and Solitons

accepted for publication in Chaos

Scientific paper

10.1063/1.1772552

We present a non-perturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behaviour of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity and scaling behavior. The results are compared with numerical simulations and show good agreement.

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