Skip to main content
SpringerLink
Log in

Permanence of a general periodic single-species system with periodic impulsive perturbations

  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

Sufficient conditions for permanence of a general periodic single-species system with periodic impulsive perturbations are obtained via comparison theory of impulsive differential equations. An application is given to the periodic impulsive logistic system.

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. D.D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications. Longman, England, 1993.

    MATH  Google Scholar 

  2. E. Funasaki and M. Kot, Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Popul. Biol.,44 (1993), 203–224.

    Article  MATH  Google Scholar 

  3. S. Gao and L. Chen, The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses. Chaos, Solitons & Fractals,24 (2005), 1013–1023.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Lakmeche, O. Arino, Birfurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dynam. Contin. Discrete Impuls.,7 (2000), 265–287.

    MATH  MathSciNet  Google Scholar 

  5. V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations. World Scientific, Singapore, 1989.

    MATH  Google Scholar 

  6. W. Li and H. Huo, Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics, J. Comput. Appl. Math.,174 (2005), 227–238.

    Article  MATH  MathSciNet  Google Scholar 

  7. W. Li and H. Huo, Existence and global attractivity of positive periodic solutions of functional differential equations with impulses. Nonlinear Analysis,59 (2004), 857–877.

    MATH  MathSciNet  Google Scholar 

  8. B. Liu, Y. Zhang and L. Chen, The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management. Nonlinear Anal. Real World Appl.,6 (2005), 227–243.

    Article  MATH  MathSciNet  Google Scholar 

  9. X. Liu and L. Chen, Global dynamics of the periodic logistic system with periodic impulsive perturbations. J. Math. Anal. Appl.,289 (2004), 279–291.

    Article  MATH  MathSciNet  Google Scholar 

  10. X. Liu and L. Chen, Global attractivity of positive periodic solutions for nonlinear impulsive systems. Nonlinear Analysis,65 (2006), 1843–1857.

    Article  MATH  MathSciNet  Google Scholar 

  11. M.G. Roberts and R.R. Kao, The dynamics of an infectious disease in a population with birth pulses. Math. Biosci.,149 (1998), 23–36.

    Article  MATH  Google Scholar 

  12. B. Shulgin, L. Stone and Z. Agur, Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol.,60 (1998), 1123–1148.

    Article  MATH  Google Scholar 

  13. S. Tang and L. Chen, Density-dependent birth rate, birth pulses and their population dynamic consequences. J. Math. Biol.,44 (2002), 185–199.

    Article  MathSciNet  Google Scholar 

  14. S. Tang and L. Chen, Global attractivity in a “food-limited” population model with impulsive effects. J. Math. Anal. Appl.,292 (2004), 211–221.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Yan, A. Zhao and J. J. Nieto, Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka—Volterra systems. Math. Comput. Model.,40 (2004), 509–518.

    Article  MATH  MathSciNet  Google Scholar 

  16. B. Zhang and Y. Liu, Global attractivity for certain impulsive delay differential equations. Nonlinear Analysis,52 (2003), 725–736.

    Article  MATH  MathSciNet  Google Scholar 

  17. W. Zhu, D. Xu and Z. Yang, Global exponential stability of impulsive delay difference equation. Appl. Math. Comput.,181 (2006), 65–72.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education) School of Mathematics and Statistics, Southwest University, 400715, Chongqing, P.R. China

    Xianning Liu

  2. Department of Systems Engineering, Shizuoka University, 432-8561, Hamamatsu, Japan

    Xianning Liu & Yasuhiro Takeuchi

Authors
  1. Xianning Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yasuhiro Takeuchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianning Liu.

Additional information

Supported by the National Natural Science Foundation of China (10571143), the Science Foundation of Southwest University (SWNUB2004001) and the Japanese Government (Monbukagakusho: MEXT) Scholarship.

About this article

Cite this article

Liu, X., Takeuchi, Y. Permanence of a general periodic single-species system with periodic impulsive perturbations. Japan J. Indust. Appl. Math. 24, 57–65 (2007). https://doi.org/10.1007/BF03167507

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03167507

Key words

Search

Navigation