Existence of Periodic Solutions in a Food Chain Model with Holling–type II Functional Response

In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin-s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

• Zhaohui Wen

• Periodic solutions
• food chain model
• coincidence degree
• time scales.

[1] Stefan Hilger. Analysis on measure chains-a unified approach to continuous
and discrete calculus. Results Math., 18(1990), 18-56.
[2] Martin Bohner, Allan Peterson. Dynamic Equations on Time Scales: An
Introduction with Applications. Boston: Birkh¨auser, 2001.
[3] Martin Bohner, Meng Fan, Jiming Zhang. Existence of periodic solutions
in predator-prey and competition dynamic systems. Nonl. Anal. RWA,
7(2006), 1193-1204.
[4] Yongkun Li, Hongtao Zhang. Existence of periodic solutions for a periodic
mutualism model on time scales. J. Math. Anal. Appl., 343(2008),
818-825.
[5] Kejun Zhuang. Periodicity for a semi-ratio-dependent predator-prey
system with delays on time scales. Int. J. Comput. Math. Sci., 4(2010),
44-47.
[6] Y.G. Sun, S.H. Saker. Positive periodic solutions of discrete three-level
food-chain model of Holling type II. Appl. Math. Comput., 180(2006),
353-365.
[7] Bingbing Zhang, Meng Fan. A remark on the application of coincidence
degree to periodicity of dynamic equtions on time scales. J. Northeast
Normal University(Natural Science Edition), 39(2007), 1-3.(in Chinese)
[8] R E Gaines, J L Mawhin. Coincidence Degree and Nonlinear Differential
Equations. Lecture Notes in Mathematics, Berlin: Springer-Verlag, 1977.