Permanence For Non-autonomous Kolmogorov System With Nonlinear Impulse

Permanence for non-autonomous Kolmogorov system with nonlinear impulse will be discussed in this article.Firstly, Chapter 1 introduces the research background and research advance about non-autonomous Kolmogorov system. Meanwhile, our research contents and methods are presented.Chapter 2 gives the sufficient conditions to ensure the permanence and global uniform attractivity of the solution of the following non-autonomous single-specie Kolmogorov system with nonlinear impulse The results generalize and improve the corresponding results in existing papers [J. Hou, Z. Teng, S. Gao, Permanence and global stability for nonautonomous N-species Lotka-Volterra competitive system with impulses, Nonlinear Anal Real World Appl, 2010,11:1882-1896] and [H. Hu, Permanence for nonautonomous predator-prey Kolmogorov systems with impulses and its applications, Appl Math Comput,2013, 223:54-75].Chapter 3 gives the sufficient conditions to ensure the permanence and ultimate boundedness of the following non-autonomous two-species Kolmogorov system with nonlinear impulse The results generalize and improve the corresponding results in existing papers [Z. Teng. Z. Li, H. Jiang, Permanence criteria in non-autonomous predator-prey Kol-mogorov systems and its applications, Dyn Syst,2004,19:171-194] and [H. Hu, Permanence for nonautonomous predator-prey Kolmogorov systems with impulses and its applications, Appl Math Comput,2013,223:54-75].