Global stability of prey-taxis systems

Hai Yang Jin, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

59 Citations (Scopus)

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 languageEnglish
Pages (from-to)1257-1290
Number of pages34
JournalJournal of Differential Equations
Volume262
Issue number3
DOIs
Publication statusPublished - 5 Feb 2017

Keywords

  • Boundedness
  • Decay rates
  • Global stability
  • Lyapunov functional
  • Predator–prey system
  • Prey-taxis

ASJC Scopus subject areas

  • Analysis

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