Self-organized pacemakers near the onset of birhythmicity

Michael Stich
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Germany

A dynamical system is birhythmic if it possesses two coexisting stable limit cycles. General amplitude equations for reaction-diffusion systems near the soft onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation are derived. The model consists of a complex Ginzburg-Landau equation coupled to a real mode. Using the phase dynamics approximation and arguments from the singular perturbation theory, it is shown that stable self-organized pacemakers, which give rise to target patterns, exist and are a generic type of spatio-temporal pattern in such a system [1,2]. Simulations not only display stable but also breathing and swinging pacemaker solutions. The drift of self-organized pacemakers in media with spatial parameter gradients is investigated analytically and numerically. Furthermore, wave instabilities of target waves are considered.

[1] M. Stich, M. Ipsen, and A. S. Mikhailov, Phys. Rev. Lett. 86(2001),4406.
[2] M. Stich, M. Ipsen, and A. S. Mikhailov, Physica D 171 (2002), 19.