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The Ising-Bloch bifurcation in two systems, the complex Ginzburg Landau equation (CGLE) and a FitzHugh Nagumo (FN) model was studied in the presence of spatial inhomogeneity. The Ginzburg Landau equation was a parametrically forced complexes and described nematic liquid crystals subjected to a rotating magnetic field and a high frequency electric field. FitzHugh Nagumo model quanlitatively modeled various chemical reactions and the front solutions were investigated in this solution. Reduced dynamical equations for the FN model were derived that explained the front dynamics close to the boundary. It was observed that the dynamics in the highly nonadiabatic limit was controllesd by the fixed points of the reduced dynamical equations.

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Physical Review E - Statistical, Nonlinear, and Soft Matter Physics