Qualitative Analysis Of A Predator-Prey Model With Two Competitive Preys And Two Predators

In this paper, global behavior of solutions for the following predator-prey model withtwo pr?edators and two competitive preys is investigatedwhere ? is a bounded region in RN with smooth boundary ?? ,ηdenotes the outwardunit normal vector on the boundary ??. The paper is divided into three sections.In Section 1, the stability of nonnegative equilibrium points for the model (1) of ODEtype is discussed.In Section 2, the uniform boundedness of global solutions and the stability of thenonnegative equilibrium points for the model of the weakly coupled reaction-di?usiontype are considered.In Section 3, using method of energy estimates and Gagliardo-Nirenberg type inequal-ities, the existence and uniform boundedness of nonnegative global solutions for the model(1) of cross-di?usion type are proved when the space dimension is one.