Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Abstract

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.

9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.html

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Cited by in corpus (5)

• Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts
• Modulated structures in electroconvection in nematic liquid crystals
• Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction-diffusion equations
• Reduction approach to the dynamics of interacting front solutions in a bistable reaction-diffusion system and its application to heterogeneous media
• Kinematic Equations for Front Motion and Spiral-Wave Nucleation