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Turing–Hopf bifurcation in a general Selkov–Schnakenberg reaction–diffusion system

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  • Li, Yanqiu
  • Zhou, Yibo

Abstract

The dynamics of a general Selkov–Schnakenberg reaction–diffusion model is investigated. We first study the globally stability of the positive equilibrium and the existence of Hopf bifurcation for the corresponding ordinary differential equation (ODE). Based on that, Turing and Turing–Hopf bifurcations due to diffusion of reaction–diffusion model are demonstrated. Using the center manifold theory and the normal form method, the bifurcation diagram of Turing–Hopf bifurcation is obtained and the spatial–temporal patterns in the different regions are considered. Numerical simulations show that the spatially homogeneous periodic, the spatially inhomogeneous and the spatially inhomogeneous periodic solutions appear.

Suggested Citation

  • Li, Yanqiu & Zhou, Yibo, 2023. "Turing–Hopf bifurcation in a general Selkov–Schnakenberg reaction–diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003740
    DOI: 10.1016/j.chaos.2023.113473
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    References listed on IDEAS

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    1. Yang, Rui, 2022. "Turing–Hopf bifurcation co-induced by cross-diffusion and delay in Schnakenberg system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
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    Cited by:

    1. Yange Wang & Xixian Bai, 2024. "An Efficient Linearized Difference Algorithm for a Diffusive Sel ′ kov–Schnakenberg System," Mathematics, MDPI, vol. 12(6), pages 1-15, March.
    2. Chen, Mengxin & Ham, Seokjun & Choi, Yongho & Kim, Hyundong & Kim, Junseok, 2023. "Pattern dynamics of a harvested predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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