Patterns dynamics in a diffusive prey–predator system with ratio-dependent functional response in a planar domain
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Published:2024-06-07
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Volume:
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ISSN:1793-5245
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Container-title:International Journal of Biomathematics
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language:en
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Short-container-title:Int. J. Biomath.
Author:
Yan Xiang-Ping1ORCID,
Zhang Cun-Hua1ORCID
Affiliation:
1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, P. R. China
Abstract
This paper is concerned with a classical two-species prey–predator reaction–diffusion system with ratio-dependent functional response and subject to homogeneous Neumann boundary condition in a two-dimensional rectangle domain. By analyzing the associated eigenvalue problem, the spatially homogeneous Hopf bifurcation curve and Turing bifurcation curve of system at the constant coexistence equilibrium are established. Then when the bifurcation parameter is in the interior of range for Turing instability and near Turing bifurcation curve, the amplitude equations of the original system near the constant coexistence equilibrium are obtained by multiple-scale time perturbation analysis. On the basis of the obtained amplitude equations, the stability and classifications of spatiotemporal patterns of the original system at the constant coexistence equilibrium are discussed. Finally, to verify the validity of the obtained theoretical results, numerical simulations are also carried out.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Gansu Province
Publisher
World Scientific Pub Co Pte Ltd