Skip to main content
SpringerLink
Log in

Periodic Orbits of n-Dimensional Impulsive Switched Systems

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we generalize the index of impulsive periodic orbits defined in planar systems to n-dimensional impulsive switched systems. The moving Poincaré section is applied, which extends the classical Poincaré section and makes it possible to always preserve the transversal property at the corresponding time t with the help of reparametrization. Further, we combine it with the implicit function theorem and linear approximation to rewrite the original n-dimensional differential equation, which contributes to the definitions of indexes of impulsive periodic orbits of arbitrary finite order m. Based on these indexes, we further obtain sufficient conditions to judge the Zhukovskiǐ quasi-stability, which permits a time lag and focuses on the study of approximate synchronization between orbits with the existence of impulsive switchings. At last, an example of harvesting fishery model with mutual impacts of infection and abrupt harvesting firstly is presented and some sufficient criteria based on model parameters are obtained to illustrate our results.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availibility

All data included in this study are available upon request by contact with the corresponding author.

References

  1. N. Bairagi, S. Bhattacharya, P. Auger, B. Sarkar, Bioeconomics fishery model in presence of infection: sustainability and demand-price perspectives. Appl. Math. Comput. 405, 126225 (2021)

    MathSciNet  Google Scholar 

  2. G.I. Bischi, F. Lamantia, D. Radi, A prey-predator fishery model with endogenous switching of harvesting strategy. Appl. Math. Comput. 219(20), 10123–10142 (2013)

    MathSciNet  Google Scholar 

  3. A. De, K. Maity, M. Maiti, An integrated project of fish and broiler: SIS model with optimal harvesting. Int. J. Biomath. 9(06), 1650088 (2016)

    Article  MathSciNet  Google Scholar 

  4. B. Ding, S. Pan, C. Ding, The index of impulsive periodic orbits. Nonlinear Anal. 192, 111659 (2020)

    Article  MathSciNet  Google Scholar 

  5. C. Ding, On the limit sets of orbits with some kinds of stabilities. Publ. Math. Debrecen. 63, 413–419 (2003)

    Article  MathSciNet  Google Scholar 

  6. C. Ding, Z. Jin, J. Soriano, Near periodicity and Zhukovskij stability. Publ. Math. Debrecen. 73, 256–363 (2008)

    Article  MathSciNet  Google Scholar 

  7. C. Ding, Lyapunov quasi-stable trajectories. Fund. Math. 220, 139–154 (2013)

    Article  MathSciNet  Google Scholar 

  8. C. Ding, Limit sets in impulsive semidynamical systems. Topol. Methods Nonlinear Anal. 43, 97–115 (2014)

    Article  MathSciNet  Google Scholar 

  9. B. Dubey, A. Patra, S.K. Sahani, Modelling the dynamics of a renewable resource under harvesting with taxation as a control variable. Appl. Appl. Math. 9(2), 592–621 (2014)

    Google Scholar 

  10. S.K. Kaul, On impulsive semidynamical systems. J. Math. Anal. Appl. 150, 120–128 (1990)

    Article  MathSciNet  Google Scholar 

  11. S.K. Kaul, On impulsive semidynamical systems II. Recursive properties. Nonlinear Anal. 16, 635–645 (1991)

    Article  MathSciNet  Google Scholar 

  12. S.K. Kaul, Stability and asymptotic stability in impulsive semidynamical systems. J. Appl. Math. Stoch. Anal. 7, 509–523 (1994)

    Article  MathSciNet  Google Scholar 

  13. V. Lakshmikantham, D.D. Baǐnov, P.S. Simeonov, Theory of Impulsive Differential Equations (World Scientific, Singapore, 1989)

    Book  Google Scholar 

  14. G.A. Leonov, Strange Attractors and Classical Stability Theory (St Petersburg university Press, Saint Petersburg, 2008), pp.81–85

    Google Scholar 

  15. H. Liu, T. Zhang, X. Li, Event-triggered control for nonlinear systems with impulse effects. Chaos Solitons Fract. 153, 111499 (2021)

    Article  MathSciNet  Google Scholar 

  16. X. Lu, H. Li, C. Wang, X. Zhang, Stability analysis of positive switched impulsive systems with delay on time scales. Int. J. Robust Nonlinear 30(16), 6879–6890 (2020)

    Article  MathSciNet  Google Scholar 

  17. S. Pan, Y. Shao, A novel approach to input-to-state stability of impulsive switched nonlinear systems. Circuits Syst. Signal Process. 41, 3739–3754 (2022)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Data Science and Artificial Intelligence, Wenzhou University of Technology, Wenzhou, 325035, Zhejiang, People’s Republic of China

    Shiyao Pan

  2. Network Information Center, Wenzhou Vocational College of Science and Technology, Wenzhou, 325035, Zhejiang, People’s Republic of China

    Ke Wu

  3. School of Mathematics, Hangzhou Normal University, Hangzhou, 310036, Zhejiang, People’s Republic of China

    Guoshun Wang

  4. School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, 265590, Shandong, People’s Republic of China

    Gang Li

Authors
  1. Shiyao Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guoshun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

SP: Conceptualization, Writing - original draft. KW: Validation, Writing-Reviewing. GL and GW: Methodology, Supervision, and Writing - reviewing and editing.

Corresponding author

Correspondence to Shiyao Pan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pan, S., Wu, K., Wang, G. et al. Periodic Orbits of n-Dimensional Impulsive Switched Systems. Circuits Syst Signal Process 43, 1414–1428 (2024). https://doi.org/10.1007/s00034-023-02546-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-023-02546-5

Keywords

Search

Navigation