Self-organized stable pacemakers near the onset of birhythmicity

Michael Stich; Mads Ipsen; Alexander S. Mikhailov

doi:10.1103/physrevlett.86.4406

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Self-organized stable pacemakers near the onset of birhythmicity

Michael Stich·Mads Ipsen·Alexander S. Mikhailov

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Abstract

General amplitude equations for reaction-diffusion systems near to the soft onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation are derived. Using these equations and applying singular perturbation theory, we show that stable autonomous pacemakers represent a generic kind of spatiotemporal patterns in such systems. This is verified by numerical simulations, which also show the existence of breathing and swinging pacemaker solutions. The drift of self-organized pacemakers in media with spatial parameter gradients is analytically and numerically investigated.

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Michael Stich, Mads Ipsen, Alexander S. Mikhailov. 2000-11-16. Self-organized stable pacemakers near the onset of birhythmicity. https://doi.org/10.1103/physrevlett.86.4406

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