Global stability of prey-taxis systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Jin, Hai-Yang¹  Wang, Zhi-An² 

[1] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

关键词: Predator-prey system;    Prey-taxis;    Boundedness;    Global stability;    Lyapunov functional;    Decay rates;   

DOI  :  10.1016/j.jde.2016.10.010

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free