Effect of boundary conditions in controlling chaos in a tri-trophic food chain with density dependent mortality in inter-mediate predator
In this paper we show the eect of the diusion and especially the Dirichlet homogenous boundary conditions in controlling chaos in a 1 tri-trophic food chain with density dependent 2 mortality in inter-mediate predator. In the corresponding ordinary reaction system we have four equilibrium points. The trivial equilibrium point E0(0; 0; 0) is unstable. Under some conditions, the axial equilibrium point E1 is locally stable and the top-predator free equilibrium point E2 and The interior point E (U; V ;W) are locally asymptotically stable. Using a global Lya-
punov function of the associated reaction diusion system, we shall prove the existence of a global attractor. We shall prove that, for diusion terms suciently large, the unstable equilibrium point becomes stable in the Lp-
norm. Furthermore we prove that it becomes the maximal attractor (i.e. one point) of the reaction diusion system.