GLOBAL BOUNDEDNESS AND STABILITY TO ATHREE-SPECIES FOOD CHAIN MODEL WITH DENSITY-DEPENDENT MOTION

In this paper, we concerned the following density-dependent three-species food chain mode {u(t)= triangle(phi(1)(v)u)-chi del center dot(u del w) +mu 1u(1-u(sigma 1)) +uv+uw, x is an element of ohm, t >0, v(t)= triangle(phi(2)(w)v) +mu(2)v(1-v(sigma 2))-b(1)uv+vw, x is an element of ohm, t >0, w(t )= triangle w+mu 3w(1-w)-b(2)uw-b(3)vw, x is an element of ohm, t >0, in a bounded domain ohm subset of R(2 )with smooth boundary and homogeneous Neu-mann boundary conditions, where all parameters were positive constants. Theglobal boundedness of classical solutions were established provided sigma(1 )> 1 and sigma(2 )> 0 under appropriate initial data. Moreover, by constructing the Lya-punov functional, it was proved that the global solution will converge to thecoexistence homogeneous steady states exponentially in L-infinity(ohm) under someassumptions on the system coefficients.