Global Dynamics of a Three-species Spatial Food Chain Model

Hai Yang Jin, Zhi An Wang, Leyun Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

51 Citations (Scopus)


In this paper, we study the following initial-boundary value problem of a three-species spatial food chain model {ut=d1Δu+u(1−u)−b1uv,x∈Ω,t>0vt=d2Δv−∇⋅(ξv∇u)+uv−b2vw−θ1v,x∈Ω,t>0wt=Δw−∇⋅(χw∇v)+vw−θ2w,x∈Ω,t>0 in a bounded domain Ω⊂R2 with smooth boundary and homogeneous Neumann boundary conditions, where all parameters are positive constants. By the delicate coupling energy estimates, we first establish the global existence of classical solutions in two dimensional spaces for appropriate initial data. Moreover by constructing Lyapunov functionals and using LaSalle's invariance principle, we establish the global stability of the prey-only steady state, semi-coexistence and coexistence steady states.

Original languageEnglish
Pages (from-to)144-183
Number of pages40
JournalJournal of Differential Equations
Publication statusPublished - 5 Oct 2022


  • Boundedness
  • Food chain
  • Global stabilization
  • Prey-taxis
  • Spatial movement

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Global Dynamics of a Three-species Spatial Food Chain Model'. Together they form a unique fingerprint.

Cite this