Skip to main content
SpringerLink
Log in

Limit cycles of a lienard cubic system with quadratic friction function

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider a Lienard cubic system with quadratic friction function and suggest a method for constructing such systems with the following distributions of limit cycles around the singular points: ((2, 0), 0), ((0, 2), 0), ((1, 1), 1), ((1, 1), 0), ((1, 0), 1), ((0, 1), 1), ((0, 0), 2), ((0, 1), 2), and ((1, 0), 2).

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. Christopher, C.J. and Lunch, S., Nonlinearity, 1999, no. 12, pp. 1099–1112.

  2. Chang Chih-fen et al., Qualitative Theory of Differential Equations, Amer. Math. Soc, vol. 100, Providence, RI, 1992.

  3. Dumortie, F. and Li, C., J. Differential Equations, 2003, vol. 188, pp. 512–554.

    Article  MathSciNet  Google Scholar 

  4. Maoan, H. et al., Adv. Ser. Dynam. Systems, 1997, vol. 15, pp. 132–183.

    Google Scholar 

  5. Zoladek, H. and Jebrane, J.M., J. Adv. Appl. Math., 1994, vol. 15, pp. 1–12.

    Article  MATH  MathSciNet  Google Scholar 

  6. Perko, L.M., Rocky Mountain Math., 1984, vol. 4, no. 3, pp. 619–644.

    MathSciNet  Google Scholar 

  7. Smale, S., Math. Intelligencer, 1998, vol. 20, no. 2, pp. 7–15.

    Article  MATH  MathSciNet  Google Scholar 

  8. Cherkas, L.A. and Sidorenko, I.N., Vesn. Magil. Dzyarzh. Univ. imya A.A. Kulyashova, 2006, no. 2–3 (24), pp. 178–182.

  9. Cherkas, L.A. and Sidorenko, I.N., Vesn. Magil. Dzyarzh. Univ. imya A.A. Kulyashova, 2007, no. 1(26), pp. 166–173.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belarus State University of Computer Science and Radio Electronics, Minsk, Belarus

    L. A. Cherkas & I. N. Sidorenko

  2. Belarus State University, Minsk, Belarus

    L. A. Cherkas & I. N. Sidorenko

Authors
  1. L. A. Cherkas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. N. Sidorenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © L.A. Cherkas, I.N. Sidorenko, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 2, pp. 217–221.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cherkas, L.A., Sidorenko, I.N. Limit cycles of a lienard cubic system with quadratic friction function. Diff Equat 44, 226–230 (2008). https://doi.org/10.1134/S0012266108020109

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266108020109

Keywords

Search

Navigation