Inhomogeneous spatial patterns for predator - Prey models: Bifurcation at a higher eigenvalue

Academic Article

Abstract

  • In this paper, we study a Rosenzweig-MacArthur predator-prey (steady-state) model with diffusion and subject to homogeneous Neumann boundary conditions. Namely, we consider the following system of elliptic equations: Δu + au - f(u) - φ(u)ν = 0 in Ω, Δν - bν + ψ(u)ν = 0 in Ω, ∂ν/∂ν = ∂ν/∂ν = 0 on ∂Ω, where Ω ⊂ Rdbl;n (n ≥ 2) is a bounded and smooth domain. We call a pair of smooth (say, C2 (Ω)) functions u(x) and ν(x) which are strictly positive and non-constant in the region Ω and satisfy the above system a spatially inhomogeneous pattern. Employing global bifurcation theory and exploring the global structure of the system, we obtain new existence results of spatially inhomogeneous patterns of large amplitude and global nature. © The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
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    Author List

  • Zou H
  • Start Page

  • 296
  • End Page

  • 323
  • Volume

  • 74
  • Issue

  • 2