Filament bifurcations in a one-dimensional model of reacting excitable fluid flow
arXiv:nlin/0302040 · doi:10.1016/S0378-4371(03)00451-5
Abstract
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 \cite{excitablePRL,excitablePRE}, 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 {\it Damk{ö}hler} 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.
9 pages, 4 figures; elsart.cls style