Target patterns in two-dimensional heterogeneous oscillatory reaction–diffusion systems

Properties of target patterns created by pacemakers, representing local regions with the modified oscillation frequency, are studied for two-dimensional oscillatory reaction–diffusion systems described by the complex Ginzburg–Landau equation. An approximate analytical solution, based on the phase dynamics approximation, is constructed for a circular core and compared with numerical results for circular and square cores. The dependence of the wavenumber and frequency of generated waves on the size and frequency shift of the pacemaker is discussed. Instabilities of target patterns, involving repeated creations of ring-shaped amplitude defects, are further considered.