Coexistence of stable particle and hole solutions for fixed parameter values in a simple reaction diffusion system

We present a simple autocatalytic reaction-diffusion model for two variables, which shows for fixed parameter values the simultaneous stable coexistence of particle solutions as well of two types of hole solutions. The associated spatially homogeneous system is characterized by the coexistence of one stable fixed point and a stable limit cycle solution. We compare our results to other dissipative systems which have for fixed parameters either stable particle or stable hole solutions including the quintic complex Ginzburg-Landau equation and the envelope equation for optical bistability as well as other reaction-diffusion models. © 2004 The American Physical Society.