ORDER-PARAMETER EQUATIONS FOR FRONT TRANSITIONS - PLANAR AND CIRCULARFRONTS

Near a parity breaking front bifurcation, small perturbations may reve rse the propagation direction of fronts. Often this results in nonstea dy asymptotic-motion, such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the pr oximity to the front bifurcation, we derive equations of motion for pl anar 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 dependen t advective field or uniform curvature (axisymmetric spots), couple th ese two degrees of freedom. In both cases this leads to a transition f rom stationary to oscillating fronts as the parity breaking bifurcatio n is approached. For axisymmetric spots, two additional dynamic behavi ors are found: rebound and collapse.