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Filament bifurcations in a one-dimensional model of reacting excitable fluid flow

Hernandez-Garcia, Emilio; Lopez, Cristobal; Neufeld, Zoltan
Physica A 327, 59-64 (2003)

Recently, it has been shown that properties of excitable media stirred by two-dimensional chaotic flows can be properly studied in a one-dimensional framework, describing the transverse profile of the filament-like structures observed in the system. Here, we perform a bifurcation analysis of this one-dimensional approximation as a function of the Damkohler number, the ratio between the chemical and the strain rates. Different branches of stable solutions are calculated, and a Hopf bifurcation, leading to an oscillating filament, identified.