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Stable spatially inhomogeneous periodic solutions for a diffusive Leslie–Gower predator–prey model

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Abstract

The main objective of this thesis is to learn about the dynamics of a diffusive Leslie–Gower predator–prey system with functional response and time delay under homogeneous Neumann boundary conditions. By in-depth analyzing eigenvalues distribution, it proves that there are (diffusion-induced, delay-induced) Turing–Hopf bifurcations around positive equilibrium state. More than this, base on the foundation of the regular modality and the center manifold theory, It is responsible for establishing a precise formula, which is to determine the Turing–Hopf bifurcation property of a diffusive Leslie–Gower predator–prey system with functional response. After that, we applied the formula to a diffusive Leslie–Gower predator–prey system with Beddington–DeAngelis functional response and time delay integrally. Finally, the results have been verified and replenished by numerical simulation adequately.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (No.11701208), the key Projects of Natural Science Research in Colleges and Universities in Anhui Province (No.2022AH051948, No.2023AH051363), the young Backbone Teachers Overseas Study and Research Funding Project in Department of Education in Anhui Province(No.JWFX2023035).

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  1. School of Mathematics and Statistics, Huangshan University, Huangshan, 245041, Anhui, People’s Republic of China

    Heping Jiang

  2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Heping Jiang

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Jiang, H. Stable spatially inhomogeneous periodic solutions for a diffusive Leslie–Gower predator–prey model. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02018-2

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