Complex-anisotropy-induced pattern formation in bistable media

A construct of anisotropy in bistable media is adopted to characterize the effects of anisotropy on pattern formation by means of anisotropic line tension. A velocity curvature relation is further derived to account for the anisotropic wave propagations. Stability analysis of transverse perturbations indicates that a sufficiently strong complex anisotropy can induce dynamical instabilities and even lead to a breakup of the wave patterns. Numerical simulations show that complex anisotropy can induce rich spatiotemporal behaviors in bistable media. The results of analysis and simulations demonstrate that this method successfully incorporates complex anisotropy into the reaction diffusion model and has general significance.