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Hopf bifurcation analysis of a reaction-diffusion Sel’kov system. (English) Zbl 1165.35027
The Sel’kov model has been used for the study of morphogenesis, population dynamics and autocatalytic oxidation reactions. The authors investigate a reaction-diffusion system known as the Sel’kov model subject to the homogeneous Neumann boundary condition, where detailed Hopf bifurcation analysis is performed. They not only show the existence of the spatially homogeneous/non-homogeneous periodic solutions of the system, but also derive conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution.

35K57Reaction-diffusion equations
34K18Bifurcation theory of functional differential equations
Full Text: DOI
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