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Author Keywords: pattern formation; reaction-diffusion systems; target patterns; KeyWords Plus: REACTION-DIFFUSION SYSTEM; GINZBURG-LANDAU EQUATION; TARGET PATTERNS; AMPLITUDE EQUATIONS; WAVE INSTABILITY; SPIRAL WAVES; MODEL; COEXISTENCE; OSCILLATION; CONVECTION
Abstract:
A birhythmic dynamical system is characterized by two coexisting stable limit cycles. In this article, a general reaction-diffusion system close to a supercritical pitchfork-Hopf bifurcation is investigated, where a soft onset of birhythmicity is possible. We show that stable self-organized pacemakers, which give rise to target patterns, exist and represent a generic type of spatio-temporal patterns in such a system. This is verified by numerical simulations which also show the existence of breathing and swinging pacemaker solutions. Stable pacemakers inhibit the formation of other pacemakers in the system. The drift of self-organized pacemakers in media with spatial parameter gradients is analytically and numerically investigated. Furthermore, instabilities induced by phase slips are also considered.
