Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65692
Title: Global stability of prey-taxis systems
Authors: Jin, HY
Wang, ZA
Keywords: Boundedness
Decay rates
Global stability
Lyapunov functional
Predator–prey system
Prey-taxis
Issue Date: 2017
Publisher: Academic Press
Source: Journal of differential equations, 2017, v. 262, no. 3, p. 1257-1290 How to cite?
Journal: Journal of differential equations 
Abstract: 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.
URI: http://hdl.handle.net/10397/65692
ISSN: 0022-0396
DOI: 10.1016/j.jde.2016.10.010
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