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Dynamics of periodic solutions in the reaction-diffusion glycolysis model: Mathematical mechanisms of Turing pattern formation

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  • Liu, Haicheng
  • Ge, Bin
  • Shen, Jihong

Abstract

A reaction-diffusion glycolysis Sel’kov model with cross-diffusion is established. It is proved that Turing instability emerges at the periodic solutions in the reaction-diffusion glycolysis model. Moreover, according to the diffusivity of glycolysis model, a formula(the first derivative formula of the minimum positive periodic solution) is established to determine that Turing patterns generated by the destabilization of periodic solutions actually depend on self-diffusion coefficient d11 and cross-diffusion coefficient d21. At last, the reliability of theoretical analysis is verified by numerical simulations.

Suggested Citation

  • Liu, Haicheng & Ge, Bin & Shen, Jihong, 2022. "Dynamics of periodic solutions in the reaction-diffusion glycolysis model: Mathematical mechanisms of Turing pattern formation," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003988
    DOI: 10.1016/j.amc.2022.127324
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    References listed on IDEAS

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    1. Duccio Fanelli & Claudia Cianci & Francesca Patti, 2013. "Turing instabilities in reaction-diffusion systems with cross diffusion," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-8, April.
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