Effect of diffusion on steady state stability of an oscillatory reaction model

Abstract

The effect of diffusion on the steady-state stability of an oscillatory chemical reaction model was investigated using stoichiometric network analysis and numerical simulations. Under both spatially uniform and nonuniform conditions, steady-state stability was investigated. Under spatially uniform conditions, the model can simulate oscillatory dynamics by passing through the Andronov-Hopf bifurcation. When diffusion is introduced into the system, the results have shown that two scenarios through which instabilities can occur are possible. Either, oscillations may be caused by the same instability as it was in homogeneous case, or, diffusion may cause new type of instability. Using the exponent polytope method, we derived a system of inequalities that describes the conditions for the emergence of both, oscillations, and diffusion-driven instabilities.