Abstract
� 2016 Elsevier Inc. 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.
Original language | English |
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Pages (from-to) | 1257-1290 |
Number of pages | 34 |
Journal | Journal of Differential Equations |
Volume | 262 |
Issue number | 3 |
DOIs | |
Publication status | Published - 5 Feb 2017 |
Keywords
- Boundedness
- Decay rates
- Global stability
- Lyapunov functional
- Predator–prey system
- Prey-taxis
ASJC Scopus subject areas
- Analysis