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Peer-reviewedCC BYInfectious Disease Modelling

Spatiotemporal dynamics in a diffusive Leslie–Gower model: Turing instability and bifurcations with prey Allee effect and predator fear effect

  • Ye Han1
  • Wanqin Wu2
  • Xuewen Tan1
  • Xinzhi Liu3
  • Wenjie Li4
4 affiliations
  1. 1School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan, 650500, China
  2. 2School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan, 650500, China; Corresponding author.
  3. 3Department of Applied Mathematics, University of Waterloo, Waterloo, N2L 3G1, Canada
  4. 4Institute for Differential Equation Theory and Applications, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, 650500, China; Corresponding author.
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Abstract

This paper deals with a diffusive Leslie–Gower model with a strong Allee effect on the prey and a fear effect on the predator. We first consider the stability of positive constant solutions of the system in the absence of diffusion. Furthermore, we analyze the Turing instability phenomenon in positive constant solutions resulting from diffusion effects. Moreover, we investigate steady-state bifurcations using the Lyapunov–Schmidt reduction. The research establishes that diffusion can induce instability in these solutions. To validate these findings, we present numerical simulations, suggesting the model's potential to generate spatial patterns under specific conditions.

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Cite

BibTeXRIS
BibTeX
@article{han2026spatiotemporal,
  title = {{Spatiotemporal dynamics in a diffusive Leslie–Gower model: Turing instability and bifurcations with prey Allee effect and predator fear effect}},
  author = {Ye Han and Wanqin Wu and Xuewen Tan and Xinzhi Liu and Wenjie Li},
  journal = {Infectious Disease Modelling},
  year = {2026},
  month = nov,
  doi = {10.1016/j.idm.2026.10.004},
  url = {https://doi.org/10.1016/j.idm.2026.10.004},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Spatiotemporal dynamics in a diffusive Leslie–Gower model: Turing instability and bifurcations with prey Allee effect and predator fear effect
AU  - Ye Han
AU  - Wanqin Wu
AU  - Xuewen Tan
AU  - Xinzhi Liu
AU  - Wenjie Li
PY  - 2026
DA  - 2026/11/05
JO  - Infectious Disease Modelling
DO  - 10.1016/j.idm.2026.10.004
UR  - https://doi.org/10.1016/j.idm.2026.10.004
AB  - This paper deals with a diffusive Leslie–Gower model with a strong Allee effect on the prey and a fear effect on the predator. We first consider the stability of positive constant solutions of the system in the absence of diffusion. Furthermore, we analyze the Turing instability phenomenon in positive constant solutions resulting from diffusion effects. Moreover, we investigate steady-state bifurcations using the Lyapunov–Schmidt reduction. The research establishes that diffusion can induce instability in these solutions. To validate these findings, we present numerical simulations, suggesting the model's potential to generate spatial patterns under specific conditions.
SN  - 2468-0427
ER  -