Boundary-driven anomalous spirals in oscillatory media

Abstract

We study a heretofore ignored class of spiral patterns in oscillatory media as characterized by the complex Landau–Ginzburg model. These spirals emerge from modulating the growth rate as a function of r , thereby turning off the instability at large r . They are uniquely determined by matching to this outer condition, lifting a degeneracy in the set of steady-state solutions of the original equations. Unlike the well-studied spiral which acts as a wave source, has a simple core structure and is insensitive to the details of the boundary on which no-flux conditions are imposed, these new spirals are wave sinks, have non-monotonic wavefront curvature near the core, and can be patterned by the form of the spatial boundary. We predict that these anomalous spirals could be produced in nonlinear optics experiments via spatially modulating the gain of the medium.

Keywords

• complex Ginzburg–Landau equation
• oscillatory media
• spiral waves
• frequency selection