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Stationary and oscillatory patterns of a food chain model with diffusion and predator-taxis
  • Renji Han,
  • Gergely Rost
Renji Han
Zhejiang University of Science and Technology

Corresponding Author:rjhan@zust.edu.cn

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Gergely Rost
University of Szeged
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Abstract

In this paper, we investigate pattern dynamics in a reaction-diffusion-chemotaxis food chain model with predator-taxis, which enriches previous studies about diffusive food chain models. By virtue of diffusion semigroup theory, we first show the global classical solvability and uniform boundedness of the considered model over a bounded domain Ω ⊂ R N ( N ≥ 1 ) with smooth boundary. Then the linear stability analysis for the considered model shows that chemotaxis can induce the unique positive spatially homogeneous steady state loses its stability via Turing bifurcation and Turing-spatiotemporal Hopf bifurcation, which results in the formation of two kinds of important spatiotemporal patterns: stationary Turing pattern and oscillatory pattern. Simultaneously, the threshold values for Turing bifurcation and Turing-spatiotemporal Hopf bifurcation are given explicitly. In addition, the existence and stability of non-constant positive steady state that bifurcates from the positive constant steady state is investigated by the abstract bifurcation theory of Crandall-Rabinowitz and eigenvalue perturbation theory. Finally, numerical simulations are performed to verify our theoretical results, and some interesting non-Turing pattern are found in temporal Hopf parameter space by numerical simulation.
27 Aug 2022Submitted to Mathematical Methods in the Applied Sciences
29 Aug 2022Submission Checks Completed
29 Aug 2022Assigned to Editor
08 Sep 2022Review(s) Completed, Editorial Evaluation Pending
09 Sep 2022Editorial Decision: Revise Minor
14 Sep 20221st Revision Received
16 Sep 2022Submission Checks Completed
16 Sep 2022Assigned to Editor
21 Sep 2022Reviewer(s) Assigned
31 Oct 2022Review(s) Completed, Editorial Evaluation Pending
02 Nov 2022Editorial Decision: Revise Minor
14 Dec 20222nd Revision Received
14 Dec 2022Submission Checks Completed
14 Dec 2022Assigned to Editor
14 Dec 2022Review(s) Completed, Editorial Evaluation Pending
20 Dec 2022Reviewer(s) Assigned
13 Jan 2023Editorial Decision: Accept