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

Haicheng Liu, Bin Ge and Jihong Shen

Applied Mathematics and Computation, 2022, vol. 431, issue C

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.

Keywords: Glycolysis Sel’kov system; Cross-diffusion; Periodic solutions; Turing instability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003988

DOI: 10.1016/j.amc.2022.127324

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