Self-organized pacemakers in birhythmic media

Michael Stich*, Mads Ipsen, Alexander S. Mikhailov

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish
    Pages (from-to)19-40
    Number of pages22
    JournalPhysica D
    Issue number1-2
    Publication statusPublished - 1 Oct 2002


    • Pattern formation
    • Reaction-diffusion systems
    • Target patterns


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