Existence and global attractivity of positive periodic solutions of competition systems. (English) Zbl 1368.34055

Zhu, Min; Lu, Shiping

J. Appl. Math. Comput. 37, No. 1-2, 635-646 (2011).

Summary: In this paper, we study the existence and global attractivity of periodic solutions of a competition system. We obtain sufficient conditions for the existence and global attractivity of positive periodic solutions by Krasnoselskii’s fixed point theorem and the construction of Lyapunov functions.

MSC:

34C25	Periodic solutions to ordinary differential equations
34D20	Stability of solutions to ordinary differential equations
47N20	Applications of operator theory to differential and integral equations
92D25	Population dynamics (general)

Keywords:

positive periodic solutions; competition system; Lyapunov function; Krasnoselskii’s fixed point theorem

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