Skip to main content
SpringerLink
Log in

Comments on “Non-existence of Shilnikov chaos in continuous-time systems”

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A paper, “Non-existence of Shilnikov chaos in continuous-time systems” was published in the journal Applied Mathematics and Mechanics (English Edition). The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.

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. Elhadj, Z. and Sprott, J. C. Non-existence of Shilnikov chaos in continuous-time systems. Applied Mathematics and Mechanics (English Edition), 33(3), 371–374 (2012) DOI 10.1007/s10483-0121556-7

    Article  MathSciNet  MATH  Google Scholar 

  2. Algaba, A., Fernández-Sánchez, F., Merino, M., and Rodríguez-Luis, A. J. Comment on “Existence of heteroclinic orbits of the Shilnikov type in a 3D quadratic autonomous chaotic system”. Journal of Mathematical Analysis and Applications, 392(1), 99–101 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Algaba, A., Fernández-Sánchez, F., Merino, M., and Rodríguez-Luis, A. J. Comment on “Silnikov chaos of the Liu system”. Chaos, 21(4), 048101 (2011)

    Article  MathSciNet  Google Scholar 

  4. Algaba, A., Fernández-Sánchez, F., Merino, M., and Rodríguez-Luis, A. J. Comment on “Heteroclinic orbits in Chen circuit with time delay”. Communications in Nonlinear Science and Numerical Simulation, 17(6), 2708–2710 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Centro de Investigación de Física Teórica y Matemática FIMAT, University of Huelva, Huelva, 21071, Spain

    A. Algaba & M. Merino

  2. Departamento de Matemática Aplicada II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, Sevilla, 41092, Spain

    F. Fernández-Sánchez & A. J. Rodríguez-Luis

Authors
  1. A. Algaba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Fernández-Sánchez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Merino
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. J. Rodríguez-Luis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. J. Rodríguez-Luis.

Additional information

Project supported by the Ministerio de Educación y Ciencia, Plan Nacional I+D+I co-financed with FEDER Funds (No.MTM2010-20907-C02) and the Consejería de Educación y Ciencia de la Junta de Andalucía (Nos. FQM-276, TIC-0130, and P08-FQM-03770)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Algaba, A., Fernández-Sánchez, F., Merino, M. et al. Comments on “Non-existence of Shilnikov chaos in continuous-time systems”. Appl. Math. Mech.-Engl. Ed. 34, 1175–1176 (2013). https://doi.org/10.1007/s10483-013-1736-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-013-1736-7

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation