COEXISTENCE AND ASYMPTOTIC PERIODICITY IN A COOPERATING MODEL

Abstract

In this paper, the cooperating two-species Lotka–Volterra model is discussed. The authors study the existence of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions and consider the existence, stability, and global attractivity of time-periodic solutions for a coupled parabolic equations in a bounded domain. Their results show that this model possesses at least one coexistence state if cross-diffusions are weak. The existence of the positive T-periodic solutions, the local stability, and the global attractivity for the parabolic system are also given.