Transition from alternating stripes to alternating labyrinths in oscillatory media

Alternating (temporally period-2) stripes and labyrinths have been observed in media of chemical and biochemical reactions; however, the mechanisms underlying the formation of these spatiotemporal patterns remain unclear. Here, we conduct computer simulation using a modified model of Belousov-Zhabotinsky reaction that incorporates a global feedback loop with a spatial strength profile of Gaussian distribution. The simulation results demonstrate that the transition from alternating stripes to alternating labyrinths occurs when the feedback is negative with a certain width of the Gaussian function. We add the same Gaussian-weighted feedback loop to an amplitude equation to describe the amplitude dynamics of the period-2 oscillation and show that the pattern dynamics of the Belousov-Zhabotinsky reaction can be well captured by this amplitude equation. Analyses of the amplitude equation demonstrate that the transition from stripes to labyrinths arises from the transverse instabilities of bistable fronts caused by the Gaussian-weighted negative global feedback.