On The Genernal Nonautonomous Predator-Prey Kolmogorov Systems

The paper studies the non-autonomous predator-prey model with modi-fied Leslie-Gower and Holling-Typeâ…¡Schemes. By introducing a new studymethod, we will estabilsh a series of new criteria on the nonnegative and ulti-mately bounded of the arbitrary solution, the uniform strong persistent of thepopulation which are described by integrable form, and the global asymptot-ically stable of any positive solution. Moreover, we extend this model to thegeneral Kolmogorov system, and obtain the criteria of the nonnegative and ulti-mately bounded of the arbitrary solution, uniform strong persistent of the pop-ulation, and the global asymptotically stable of any positive solution. We alsoconsider the nonautonomous predator-prey model with modified Leslie-Gowerand Holling-Typeâ…¡Schemes and time delays. We get a series of criteria fornonnegative boundedness of the nonnegative and ultimately bounded of the ar-bitrary solution, the uniform strong persistent of the population, and the globalasymptotically stable of any positive solution.