期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 262, 期 3, 页码 1257-1290出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2016.10.010
关键词
Predator-prey system; Prey-taxis; Boundedness; Global stability; Lyapunov functional; Decay rates
类别
资金
- NSF of China [11501218]
- China Postdoctoral Science Foundation [2015M572302]
- Fundamental Research Funds for the Central Universities [2015ZM088]
- Hong Kong RGC GRF [PolyU 153298/16P]
In this paper, we prove the global boundedness and stability of the predator-prey system with prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions. By deriving an entropy-like equality and a boundedness criterion, we show that the intrinsic interaction between predators and preys is sufficient to prevent the population overcrowding even the prey-taxis is included and strong. Furthermore, by constructing appropriate Lyapunov functionals, we show that prey-only steady state is globally asymptotically stable if the predation is weak, and the co-existence steady state is globally asymptotically stable under some conditions (like the prey-taxis is weak or the prey diffuses fast) if the predation is strong. The convergence rates of solutions to the steady states are derived in the paper. (C) 2016 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据