Electron. J. Diff. Equ., Vol. 2012 (2012), No. 199, pp. 1-13.

Necessary and sufficient conditions for the existence of periodic solutions in a predator-prey model on time scales

Xingyong Liu, Xiuxiang Liu

Abstract:
This article explores the existence of periodic solutions for non-autonomous impulsive semi-ratio-dependent predator-prey systems on time scales. Based on a continuous theorem in coincidence degree theory, sharp sufficient and necessary conditions are derived in which most popular monotonic, non-monotonic and predator functional responses are applicable. This article extends the work in [6,10,12,13,134,18,25].

Submitted July 16, 2012. Published November 15, 2012.
Math Subject Classifications: 34A34, 34C25, 92D25.
Key Words: Time scales; periodic solutions; predator-prey system; functional responses.

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Xingyong Liu
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: 32553961@qq.com
Xiuxiang Liu
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: liuxx@scnu.edu.cn

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