Global dynamics and spatio-Temporal patterns of predator-prey systems with density-dependent motion

Hai Yang Jin, Zhi An Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)

Abstract

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent prey-Taxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusiq'dfdon) and mobility (prey-Taxis) of the predator are correlated through a prey density-dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals. With numerical simulations, we further demonstrate that spatially homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns and chaotic spatio-Temporal patterns are all possible for the parameters outside the stability regime. We also find from numerical simulations that the temporal dynamics between linearised system and nonlinear systems are quite different, and the prey density-dependent motility function can trigger the pattern formation.

Original languageEnglish
Pages (from-to)652-682
Number of pages31
JournalEuropean Journal of Applied Mathematics
Volume32
Issue number4
DOIs
Publication statusE-pub ahead of print - 12 Aug 2020

Keywords

  • boundedness
  • global stability
  • Lyapunov functional
  • Predator-prey system
  • prey-Taxis

ASJC Scopus subject areas

  • Applied Mathematics

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