Skip to main content
Log in

Existence of at Least Two Periodic Solutions of a Ratiodependent Predator-prey Model with Exploited Term

  • Original Papers
  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

In this paper, we study a non-autonomous ratio-dependent predator-prey model with exploited term. By means of the coincidence degree theory, we establish a sufficient condition for the existence of at least two positive periodic solutions of this model.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Arditi, R., Ginzburg, L.R. Coupling in predator-prey dynamics:ratio-dependence. J. Ther. Biol., 139:311–326 (1989)

    Article  Google Scholar 

  2. Berryman, A.A. The origins and evolution of predator-prey theory. Ecology, 75:1530–1535 (1992)

    Article  Google Scholar 

  3. Fan, M., Wang, Q., Zou, X. Dynamics of a non-autonomous ratio-dependent predator-prey system. Proceedings of the Royal Society of Edinburgh, 133A:97–118 (2003)

    Google Scholar 

  4. Gaines, R.E., Mawhin, J.L. Coincidence degree and non-linear differential equations. Springer-Verlag, Berlin, 1977

  5. Ma, Z. Mathematical modeling and studying on species ecology. Education Press, Hefei, 1996 (in Chinese)

  6. Zhang, Z., Zeng, X. A periodic stage-structure Model. App. Math. Letters, 16:1053–1061 (2003)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to De-sheng Tian.

Additional information

Supported by the National Natural Science Foundation of China (No.19531070)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian, Ds., Zeng, Xw. Existence of at Least Two Periodic Solutions of a Ratiodependent Predator-prey Model with Exploited Term. Acta Mathematicae Applicatae Sinica, English Series 21, 489–494 (2005). https://doi.org/10.1007/s10255-005-0256-5

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-005-0256-5

Keywords

2000 MR Subject Classification

Navigation