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Pattern formation in a predator-prey model

2019-12-27 08:38

报告人: 王玮明

报告人单位: 淮阴师范学院数学科学学院

时间: 2019-12-14 14:30-15:3

地点: 天津大学卫津路校区第十四教学楼214室

开始时间: 14:30

报告人简介: 教授

年: 2019

日月: 12.14

In this talk, I will introduce some new results on the spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge subject to the Neumann boundary conditions. We mainly consider Hopf bifurcation and steady-state bifurcation which bifurcate from the constant positive steady-state of the model. In the case of Hopf bifurcation, by the center manifold theory and the normal form method, we establish the bifurcation direction and stability of bifurcating periodic solutions; in the case of steady-state bifurcation, by the local and global bifurcation theory, we prove the existence of the steady-state bifurcation, and find that there are two typical bifurcations, Turing bifurcation and Turing-Hopf bifurcation. Via numerical simulations, we find that the model exhibits not only stationary Turing pattern induced by diffusion which is dependent on space and independent of time, but also temporal periodic pattern induced by Hopf bifurcation which is dependent on time and independent of space, and spatiotemporal pattern induced by Turing-Hopf bifurcation which is dependent on both time and space. These results may enrich the pattern formation in the predator-prey model.

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