Interaction of Ising-Bloch fronts with Dirichlet Boundaries

Details Interaction of Ising-Bloch fronts with Dirichlet Boundaries Interaction of Ising-Bloch fronts with Dirichlet Boundaries

2004-04-26

arxiv.org/abs/nlin/0404046v1

Nonlinear Sciences

Pattern Formation and Solitons

10 pages, 8 figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.70.036218

We study the Ising-Bloch bifurcation in two systems, the Complex Ginzburg Landau equation (CGLE) and a FitzHugh Nagumo (FN) model in the presence of spatial inhomogeneity introduced by Dirichlet boundary conditions. It is seen that the interaction of fronts with boundaries is similar in both systems, establishing the generality of the Ising-Bloch bifurcation. We derive reduced dynamical equations for the FN model that explain front dynamics close to the boundary. We find that front dynamics in a highly non-adiabatic (slow front) limit is controlled by fixed points of the reduced dynamical equations, that occur close to the boundary.

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