Abstract
We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ma Zhien. Mathematical Modeling and Mtudying on Species Ecology[M]. Hefei: Anhui Education Press, 1996: 337–339(Ch).
Arditi R, Ginzburg L R. Coupling in Predator-Prey Dynamics: Ratio-Dependence[J]. J Ther Biol, 1989, 139:311–326.
Fan Meng, Wang Qian, Zou X. Dynamics of a Non-Autonomous Ratio-Dependent Predator-Prey Dystem[J]. Proceedings of the Royal Society of Edinburgh, 2003, 133A: 97–118.
Berryman A A. The Origins and Evolution of Predator-Prey Theory[J]. Ecology, 1992, 75:1530–1535.
Tian Desheng, Zeng Xianwu. Existence of at least Two Periodic Solutions of a Ratio-Dependent Predator-Prey Model with Exploited Term[J]. Acta Math Appl Sinica, English Series, 2005, 21(3): 489–494.
Zhang Zhengqiu, Zeng Xianwu. A Periodic Stage-Structure Model[J]. App Math Letters, 2003, 16: 1053–1061.
Tian Desheng, Zeng Xianwu. Periodic Solutions of a Class of Predator-Prey Model Exploited with Functional Response[J]. J of Math (PRC), 2005, 25(5): 480–484.
Zhang Zhengqiu, Wang Zhicheng. Periodic Solutions of a Two-Species Ratio-Dependent Predator-Prey System with Time Delay in a Two-Patch Environment[J]. ANZIAM J, 2003, 45: 233–244.
Chen Yuming. Multiple Periodic Solutions of Delayed Predator-Prey System with Type-IV Functional Response[J]. Nonlinear Anal: Real world Appl, 2004, 45(5):45–53.
Gaines R E, Mawhin J L. Coincidence Degree and Non-Linear Differential Equations[M]. Berlin: Springer-Verlag, 1977.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Supported by the China Postdoctoral Science Foundation (20060400267)
Biography: TIAN Desheng(1966–), male, Associate professor, Ph. D., research direction: qualitative theory of differential equation.
Rights and permissions
About this article
Cite this article
Tian, D., Zhang, Z. Existence of four periodic solutions of a ratio-dependent predator-prey model with exploited terms. Wuhan Univ. J. Nat. Sci. 13, 1–5 (2008). https://doi.org/10.1007/s11859-008-0101-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11859-008-0101-9