Self-organized pacemakers near the onset of birhythmicity
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.
M. Stich, M. Ipsen, and A. S. Mikhailov, Phys. Rev. Lett. 86(2001),4406.
 M. Stich, M. Ipsen, and A. S. Mikhailov, Physica D 171 (2002), 19.