×

zbMATH — the first resource for mathematics

The effect of interaction ratio in a chemical reaction. (English) Zbl 1284.35452
Summary: This paper is concerned with the effect of interaction ratio in a chemical reaction with zero-flux boundary condition. Treating the interaction ratio \(\gamma \) as a parameter, the existence of non-constant positive steady states is discussed by the bifurcation theory. Especially, the steady-state bifurcation from the double eigenvalue is derived. The Hopf bifurcation analysis to both ordinary differential equations and partial differential equations systems is investigated in detail. Examples of numerical simulations are shown to support and complement the analytical conclusions.

MSC:
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92E20 Classical flows, reactions, etc. in chemistry
35K57 Reaction-diffusion equations
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
35P99 Spectral theory and eigenvalue problems for partial differential equations
34B09 Boundary eigenvalue problems for ordinary differential equations
35B32 Bifurcations in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI