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Hopf bifurcation and periodic solutions in a coupled Brusselator model of chemical reactions

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Abstract

In this paper, we consider a coupled Brusselator model of chemical reactions, for which no symmetry for the coupling matrices is assumed. We show that the model can undergo a Hopf bifurcation, and consequently periodic solutions can arise when the dispersal rates are large. Moreover, the effect of the coupling matrices on the Hopf bifurcation value is considered for a special case.

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Funding

This study was funded by National Natural Science Foundation of China (Grant Number 12171117) and Shandong Provincial Natural Science Foundation of China (Grant Number ZR2020YQ01).

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Authors and Affiliations

  1. School of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People’s Republic of China

    Yihuan Sun

  2. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, Shandong, People’s Republic of China

    Shanshan Chen

Authors
  1. Yihuan Sun
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  2. Shanshan Chen
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Contributions

All authors contributed to the study conception and design. SC developed the idea for the study. The manuscript was written by SC and YS. YS prepared Figs. 1, 2, 3, 4, 5 and 6. All authors read and approved the final manuscript.

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Correspondence to Shanshan Chen.

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Sun, Y., Chen, S. Hopf bifurcation and periodic solutions in a coupled Brusselator model of chemical reactions. J Math Chem 62, 169–197 (2024). https://doi.org/10.1007/s10910-023-01528-x

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