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.
|Number of pages
|Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|Published - 1 Jan 1997
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics