Target Patterns and Spirals in Planar Reaction-Diffusion Systems

wall

modes. In contrast, if the boundary conditions are Neumann or Dirichlet, then the eigenfunctions are defined by Bessel functions of real argument, and take the form of body modes filling the interior of the domain. Body modes typically do not exhibit pronounced spiral structure. We argue that the wall modes are important for understanding the formation process of spirals, even in extended systems. Specifically, we conjecture that wall modes describe the core of the spiral; the constant-amplitude spiral visible outside the core is the result of strong nonlinearities which enter almost immediately above threshold as a consequence of the exponential radial growth of the wall modes.