Turing instability of the periodic solutions for the diffusive Sel’kov model with saturation effect. (English) Zbl 1479.35073
Summary: In this paper, we are concerned with the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions for the diffusive Sel’kov model with saturation effect. By using the center manifold theorem, normal form theory and the regularly perturbed theory, we derive a formula in terms of the diffusion rates to determine the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions in the reaction-diffusion system. Moreover, we compare our results with those of equilibrium solutions to demonstrate the differences between Turing instability of the equilibrium solutions and the periodic solutions.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 92E20 | Classical flows, reactions, etc. in chemistry |
Keywords:
homogeneity breaking instability; spatially homogeneous Hopf bifurcating periodic solutions; chemical reactionsReferences:
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