Dynamical Analysis Of A Predator-prey Model With Dissipative Structure

Today, the ability of changing the nature is greatly heightened. The ecologi-cal balance is destroyed seriously. It is important to analyze the behavior of thepredator-prey model, according to the application in the nature. In particular, itis focused on the equilibrium solution of the predator-prey model, the existence ofperiodic solution and stability.In this paper, we study the predator-prey model with dissipative structure:where k, a, δ2are positive constants, is a bounded domain in RN(N≥1), and theboundary is smooth. We study the conditions of Hopf bifurcation generated bythe system, by using the Hopf bifurcation theory to determine the direction of Hopfbifurcation and stability of periodic solutions.We also study the steady-state system:By analyzing the conditions of steady-state bifurcation generated by the system,we obtain global steady-state bifurcation solutions of the predator-prey model withdissipative structure, according to the steady-state bifurcation theorem.