Periodic Solutions for a Delayed Population Model on Time Scales

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062700

References:

[1] V G Nazarenko. Influence of delay on auto-oscillation in cell populations. Biofisika, 21(1976), 352-356.
[2] Yongli Song, Yahong Peng. Periodic solutions of a nonautonomous periodic model of population with continuous and discrete time. J. Comp. Appl. Math., 188(2006), 256-264.
[3] S H Saker. Periodic solutions, oscillation and attractivity of discrete nonlinear delay population model. Math. Comput. Model., 2008, 47: 278- 297.
[4] Martin Bohner, Allan Peterson. Dynamic Equations on Time Scales: An Introduction with Applications. Boston: Birkh¨auser, 2001.
[5] Stefan Hilger. Analysis on measure chains-a unified approach to continuous and discrete calculus. Results Math., 18(1990), 18-56.
[6] Martin Bohner, Meng Fan, Jiming Zhang. Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear Anal. RWA, 7(2006), 1193-1204.
[7] 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.
[8] 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)
[9] R E Gaines, J L Mawhin. Coincidence Degree and Nonlinear Differential Equations. Lecture Notes in Mathematics, Berlin: Springer-Verlag, 1977.