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Multi-stable and spatiotemporal staggered patterns in a predator-prey model with predator-taxis and delay
  • Weihua Jiang,
  • Yue Xing|,
  • Xun Cao
Weihua Jiang
Harbin Institute of Technology School of Mathematics

Corresponding Author:jiangwh@hit.edu.cn

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Yue Xing|
Harbin Institute of Technology School of Mathematics
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Xun Cao
Harbin Institute of Technology School of Mathematics
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Abstract

The effects of predator-taxis and conversion time delay on formations of spatiotemporal patterns in a predator-prey model are explored. Firstly, the well-posedness, which implies global existence of classical solutions, is proved. Then, we establish critical conditions for the destabilization of coexistence equilibrium through Turing/Turing-Turing bifurcations via describing the first Turing bifurcation curve, and theoretically predict possible bi-stable/multi-stable spatially heterogeneous patterns. Next, we demonstrate that coexistence equilibrium can also be destabilized through Hopf, Hopf-Hopf, Turing-Hopf bifurcations, and possible stable/bi-stable spatially inhomogeneous staggered periodic patterns, bi-stable spatially inhomogeneous synchronous periodic patterns, are theoretically predicted. Finally, numerical experiments also support theoretical predictions and partially extend them. In a word, theoretical analyses indicate that, on the one hand, large predator-taxis can eliminate spatial patterns caused by self-diffusion; on the other hand, the joint effects of predator-taxis and conversion time delay can induce complex survival patterns, e.g., bi-stable spatially heterogeneous staggered/synchronous periodic patterns, thus diversify populations’ survival patterns.
12 Jan 2023Submitted to Mathematical Methods in the Applied Sciences
12 Jan 2023Assigned to Editor
12 Jan 2023Submission Checks Completed
18 Jan 2023Review(s) Completed, Editorial Evaluation Pending
22 Jan 2023Reviewer(s) Assigned