期刊
JOURNAL OF BIOLOGICAL SYSTEMS
卷 28, 期 3, 页码 785-809出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218339020500175
关键词
Predator-Prey Model; Diffusion; Turing Instability; Hopf Bifurcation; Turing-Hopf Bifurcation
资金
- National Natural Science Foundation of China [11461040, 11401245]
- Natural Science Foundation of Jiangsu Province [BK20151288]
- Postdoctoral Science Foundation of Jiangsu Province [1401063C]
- Postdoctoral Science Foundation of China [2014M561717]
- Natural Science Research Plan of Huaian City [HABZ201918]
In this paper, we study the spatiotemporal dynamics of a diffusive Leslie-type predator-prey system with Beddington-DeAngelis functional response under homogeneous Neumann boundary conditions. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential equations is presented. For the diffusive model, firstly, it is shown that Turing (diffusion-driven) instability occurs which induces spatial inhomogeneous patterns. Next, it is proved that the diffusive model exhibits Hopf bifurcation which produces temporal inhomogeneous patterns. Furthermore, at the points where the Turing instability curve and Hopf bifurcation curve intersect, it is demonstrated that the diffusive model undergoes Turing-Hopf bifurcation and exhibits spatiotemporal patterns. Numerical simulations are also presented to verify the theoretical results.
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