On The General Nonautonomous Predator-prey Kolmogorov Systems

The paper studies the general nonautonomous predator-prey Kolmogorov sys-tems. As a continuation of the work [23], we will investigate the equivalence of the permanence and strong persistence, By introducing a new study method, we will establish a series of new criteria on the average persistence and extinction of positive solutions which are described by integrable form, and also investigate the equivalence of the uniformly weak average persistence and the weak average persistence. We will prove the equivalence of permanence, strong persistence, uniformly strong average persistence, unifornily weak average persistence, strong average persistence and weak average persistence for the periodic systems and almost periodic systems. Further, as applications of these results, the sufficient conditions of integrable form on the average persistence and extinction will be obtained for nonautonomous Lotka-Volterra type systems, Holling (m,n)-type functional response systems, Beddington-DeAngelis functional response systems and Ghemos'tat-type systems, the equivalence of the permanence, strong persis-tence, uniformly strong average persistence, uniformly weak average persistence, strong average persistence and weak average persistence for these systems under the periodic and almost periodic cases will also be discussed.