Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
837892 | Nonlinear Analysis: Real World Applications | 2011 | 16 Pages |
Abstract
In this paper, we investigate the existence, stability, permanence, and global attractor of positive solutions for the following three species food chain model with diffusion and Beddington–Deangelis functional response {−Δu1=u1(r−u1)−a1u1u2e1+u1+u2inΩ,−Δu2=m1u1u2e1+u1+u2−b1u2−a2u2u3e2+u2+u3inΩ,−Δu3=m2u2u3e2+u2+u3−b2u3inΩ,k1∂u1∂ν+u1=k2∂u2∂ν+u2=k3∂u3∂ν+u3=0on∂Ω, where ΩΩ is a bounded domain of RNRN, N≥1N≥1, with boundary ∂Ω∂Ω of class C2+αC2+α for some α∈(0,1)α∈(0,1), νν is the outward unit vector on ∂Ω∂Ω, the parameters r,ai,bi,ei,mi(i=1,2) are strictly positive, and ki≥0(i=1,2,3), ui(i=1,2,3) are the respective densities of prey, predator, and top predator.
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Authors
Jun Zhou, Chunlai Mu,