一类自催化可逆生化反应模型的Hopf分支及其稳定性

Abstract

Abstract:

An autocatalytic reversible three-molecular biochemical reaction model subject to Neumann boundary conditions is considered. Firstly, the existence and stability of the Hopf bifurcation for the ordinary differential system are given. Secondly, the effect of diffusion coefficients on Turing instability is established and the existence of Hopf bifurcation is obtained for the partial differential system with diffusion. Then applying the normal form theory and center manifold theorem, the direction and stability of Hopf bifurcation are also given. Finally, some numerical simulations are carried out with the help of Matlab software to verify and supplement the theoretical results.

Key words: Reversible biochemical reaction, Turing instability, Hopf bifurcation, Stability

CLC Number:

O175.26

Gaihui Guo,Xiaohui Liu. Hopf Bifurcation and Stability for an Autocatalytic Reversible Biochemical Reaction Model[J].Acta mathematica scientia,Series A, 2021, 41(1): 166-177.

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Figures/Tables 6

References 13

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Hopf Bifurcation and Stability for an Autocatalytic Reversible Biochemical Reaction Model

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