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Turing-Hopf bifurcation of a diffusive Holling-Tanner model with nonlocal effect and digestion time delay
  • Yehu Lv
Yehu Lv
Beijing Normal University School of Mathematical Sciences

Corresponding Author:mathyehul@163.com

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Abstract

In this paper, we discuss the Turing-Hopf bifurcation of a diffusive Holling-Tanner model with nonlocal effect and digestion time delay. The stability, Turing bifurcation, Hopf bifurcation and Turing-Hopf bifurcation are first researched. Then we derive the algorithm for calculating the normal form of Turing-Hopf bifurcation of a diffusive Holling-Tanner model with nonlocal effect and digestion time delay. At last, we carry out some numerical simulations to verify our theoretical analysis results. The stable positive constant steady state and the stable spatially inhomogeneous periodic solutions are found. Furthermore, the evolution process from unstable spatially inhomogeneous steady states to stable positive constant steady state, the evolution process from unstable spatially inhomogeneous steady states to stable spatially inhomogeneous periodic solutions, the evolution process from one unstable spatially inhomogeneous periodic solution to another stable spatially inhomogeneous periodic solution and the evolution process from unstable spatially inhomogeneous periodic solution to stable positive constant steady state are also found.
08 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
09 Mar 2022Submission Checks Completed
09 Mar 2022Assigned to Editor
19 Mar 2022Reviewer(s) Assigned
09 Dec 2022Editorial Decision: Revise Minor
10 Dec 20221st Revision Received
12 Dec 2022Submission Checks Completed
12 Dec 2022Assigned to Editor
12 Dec 2022Review(s) Completed, Editorial Evaluation Pending
14 Dec 2022Reviewer(s) Assigned
08 Feb 2023Editorial Decision: Accept