Skip to main content
SpringerLink
Log in

Existence of four periodic solutions of a ratio-dependent predator-prey model with exploited terms

  • Published:
Wuhan University Journal of Natural Sciences

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ma Zhien. Mathematical Modeling and Mtudying on Species Ecology[M]. Hefei: Anhui Education Press, 1996: 337–339(Ch).

    Google Scholar 

  2. Arditi R, Ginzburg L R. Coupling in Predator-Prey Dynamics: Ratio-Dependence[J]. J Ther Biol, 1989, 139:311–326.

    Article  Google Scholar 

  3. 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.

    Article  MathSciNet  Google Scholar 

  4. Berryman A A. The Origins and Evolution of Predator-Prey Theory[J]. Ecology, 1992, 75:1530–1535.

    Article  Google Scholar 

  5. 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.

    Article  MathSciNet  Google Scholar 

  6. Zhang Zhengqiu, Zeng Xianwu. A Periodic Stage-Structure Model[J]. App Math Letters, 2003, 16: 1053–1061.

    Article  MATH  Google Scholar 

  7. 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.

    MATH  MathSciNet  Google Scholar 

  8. 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.

    Article  MATH  MathSciNet  Google Scholar 

  9. 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.

    Article  Google Scholar 

  10. Gaines R E, Mawhin J L. Coincidence Degree and Non-Linear Differential Equations[M]. Berlin: Springer-Verlag, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Hubei University of Technology, Wuhan, 430068, Hubei, China

    Desheng Tian

  2. Department of Applied Mathematics, Hunan University, Changsha, 410082, Hunan, China

    Zhengqiu Zhang

Authors
  1. Desheng Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengqiu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Desheng Tian.

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

Reprints 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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-008-0101-9

Key words

CLC number

Search

Navigation