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Bifurcation and Turing instability for a freshwater tussock sedge model with nonlocal interaction

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Abstract

The Hopf bifurcation, Turing instability and steady state bifurcation to a fresh-water tussock sedge model with nonlocal interaction under Neumman boundary condition are investigated in this paper. First, we analyze the existence of constant steady states and the effect of the nonlocal term on the its stability and the existence of Hopf bifurcation. Furthermore, the occurrence conditions of Turing instability to such system are studied. Second, we focus on steady state bifurcation to the reaction–diffusion system with nonlocal interaction via Lyapunov–Schmidt reduced method. Finally, numerical simulations have been illustrated to verify our theoretical analysis.

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Acknowledgements

The authors would like to thank the editor and the referees for their helpful comments. This research was supported by the National Natural Science Foundation of China (nos. 12101005, 12301172, 11971032), the Scientific Research Foundation of Anhui Provincial Education Department (nos. KJ2020A0483, 2023 AH050191) and the PhD Research Startup Fund for Anhui Jianzhu University (No. 2019QDZ25, 2022QDZ19).

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Authors and Affiliations

  1. School of Mathematics and Physics, Anhui Jianzhu University, Hefei, 230601, Anhui, People’s Republic of China

    Biao Liu

  2. Operations Research and Data Science Laboratory, Anhui Jianzhu University, Hefei, People’s Republic of China

    Biao Liu

  3. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, People’s Republic of China

    Quanli Ji & Ranchao Wu

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  1. Biao Liu
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  2. Quanli Ji
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Correspondence to Biao Liu.

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Liu, B., Ji, Q. & Wu, R. Bifurcation and Turing instability for a freshwater tussock sedge model with nonlocal interaction. Comp. Appl. Math. 43, 263 (2024). https://doi.org/10.1007/s40314-024-02783-7

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  • DOI: https://doi.org/10.1007/s40314-024-02783-7

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