Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis

In this preliminary paper we introduce a mathematical model based on an autocatalytic reaction scheme with termination, and general reaction orders. Rigorous stability analysis and numerical solutions are presented which illustrate that the problem can for certain parameter values admit a stable stationary pattern in the concentration of the autocatalyst and reactant. This pattern forms at the rear of a permanent form travelling wave or pulse solution.