 Stationary pattern and bifurcation of a Leslie–Gower predator–prey model with prey-taxisXiao Yan, Yimamu Maimaiti and Wenbin Yang Mathematics and Computers in Simulation (MATCOM), 2022, vol. 201, issue C, 163-192 Abstract: In this paper, we consider a Leslie–Gower predator–prey model with prey-taxis subject to the homogeneous Neumann boundary condition. First, the stability of positive constant solution for corresponding ODE and PDE models is studied, respectively. It turns out that small prey-taxis can cause Turing instability and produce spatio-temporal patterns; large prey-taxis can stabilize the instability caused by diffusion. Then, in spatial one dimension, we use the center manifold theory to analyze the direction of Hopf bifurcation and stability of the bifurcation periodic solutions. By regarding prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of non-constant solutions bifurcating from the positive equilibrium and find the stability criterion of such bifurcation solutions. Finally, some numerical simulations are shown to verify and expand our theoretical findings. Keywords: Predator–prey model; Prey-taxis; Stationary pattern; Bifurcation; Numerical simulation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:201:y:2022:i:c:p:163-192 DOI: 10.1016/j.matcom.2022.05.010 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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