Abstract

The coexistence of fixed parameter values in dissipative evolution equations stable particle and hole solutions for a simple autocatalytic reaction-diffusion model, was analyzed. The analysis of the spatially homogeneous system was done by calculating the coexistence of one stable fixed point and a stable limit cycle solution. The results obtained through the calculation were compared to other dissipative systems which have for fixed parameters either stable particle or stable hole solutions including the quintic complex Ginzburg-Landau equation. It was observed that in this rapid communication three different types of localized solution can stably occur for fixed set of parameter values.