Dynamic behaviors of an obligate Gilpin-Ayala system

Advances in Difference Equations

Danhong Wang¹ 

[1] Department of Mathematics, Minjiang University, Fuzhou, P.R. China

关键词: obligate Gilpin-Ayala system;    extinction;    permanence;    Lyapunov function;    global attractivity;    34C25;    92D25;    34D20;    34D40;   

DOI  :  10.1186/s13662-016-0965-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a nonautonomous obligate Gilpin-Ayala system is proposed and studied. The persistence and extinction of the system are discussed by using the comparison theorem of differential equations. The results show that, depending on the cooperation intensity between the species, the first species will be driven extinct or be permanent. After that, by using the Lyapunov function method, series of sufficient conditions are obtained which ensure the global attractivity of the system. Finally, two examples are given to illustrate the feasibility of the main results.

【 授权许可】

CC BY