Skip to main content

Oscillatory Behavior of the Solutions for a Coupled van der Pol-Duffing Oscillator with Delay

  • Conference paper
  • First Online:
Intelligent Computing Theories and Methodologies (ICIC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9226))

Included in the following conference series:

  • 1519 Accesses

Abstract

This paper studies the oscillatory behavior for a coupled van der Pol-Duffing oscillator with delay. Two theorems are provided to guarantee the oscillation of the system. Computer simulations are given to support the theoretical analysis.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Li, X.Y., Ji, J.C., Hansen, C.H.: Dynamics of two delay coupled van Der Pol oscillators. Mech. Res. Commun. 33, 614–627 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhang, J.M., Gu, X.S.: Stability and bifurcation analysis in the delay-coupled van Der Pol oscillators. Appl. Math. Model. 34, 2291–2299 (2010)

    Article  MathSciNet  Google Scholar 

  3. Sabarathinam, S., Thamilmaran, K., Borkowski, L., Perlikowski, P., Bzeski, P., Stefanski, A., Kapitaniak, T.: Transient chaos in two coupled, dissipatively perturbed Hamiltonian duffing oscillators. Commun. Nonlinear. Sci. Numer. Simul. 18, 3098–3107 (2013)

    Article  MathSciNet  Google Scholar 

  4. Kuznetsov, A.P., Stankevich, N.V., Turukina, L.V.: Coupled van der Pol-Duffing oscillators: phase dynamics and structure of synchronization tongues. Physica D 238, 1203–1215 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kuznetsov, A.P., Paksyutov, V.I.: Feature of the parameter space structure of two non -identical coupled van der Pol-Duffing oscillators. Appl. Nonlin. Dynam. 13, 3–19 (2005)

    Google Scholar 

  6. Peano, V., Thorwart, M.: Dynamics of the quantum duffing oscillator in the driving induced bistable regime. Chem. Phys. 322, 135–143 (2006)

    Article  MATH  Google Scholar 

  7. Camacho, E., Rand, R.H., Howland, H.: Dynamics of two van der Pol oscillators coupled via a bath. Int. Solids Struct. 41, 2133–2143 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kuznetsov, A.P., Paksyutov, V.I., Roman, Y.P.: Features of the synchronization of coupled van der Pol oscillators with nonidentical control parameters. Tech. Phys. Lett. 8, 636–638 (2007)

    Article  MATH  Google Scholar 

  9. Gendelman, O.V., Starosvetsky, Y.: Quasiperiodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing. Trans. ASME J. Appl. Mech. 74, 325–331 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rusinek, R., Weremczuk, A., Kecik, K., Warminski, J.: Dynamics of a time delayed Duffing oscillator. Int. J. Nonlin. Mech. 65, 98–106 (2014)

    Article  Google Scholar 

  11. Siewe Siewe, M., Tchawoua, C., Rajasekar, S.: Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback. Commun. Nonlinear Sci. Num. Simul. 17, 4485–4493 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Beregov, R.Y., Melkikh, A.V.: De-synchronization and chaos in two inductively coupled Van der Pol auto-generators. Chaos Solitons Fractals 73, 17–28 (2015)

    Article  MathSciNet  Google Scholar 

  13. Sun, Y., Xu, J.: Experiments and analysis for a controlled mechanical absorber considering delay effect. J. Sound Vibr. 339, 25–37 (2015)

    Article  Google Scholar 

  14. Zhang, C.M., Li, W.X., Wang, K.: Boundedness for network of stochastic coupled van Der Pol oscillators with time-varying delayed coupling. Appl. Math. Model. 37, 5394–5402 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Horn, R.A., Johnso, C.R.: Matrix Analysis. Cambridge Press, Cambridge (1990)

    MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by NNSF of China (11361010), the high school specialty and curriculum integration project of Guangxi Zhuang Autonomous Region (GXTSZY2220), the SRF of the Education Department of Guangxi Province (LX2014330), and the Key Discipline of Statistics of Hechi University of China (20133).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuanhua Lin .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Lin, Y., Hou, Z. (2015). Oscillatory Behavior of the Solutions for a Coupled van der Pol-Duffing Oscillator with Delay. In: Huang, DS., Jo, KH., Hussain, A. (eds) Intelligent Computing Theories and Methodologies. ICIC 2015. Lecture Notes in Computer Science(), vol 9226. Springer, Cham. https://doi.org/10.1007/978-3-319-22186-1_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22186-1_47

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22185-4

  • Online ISBN: 978-3-319-22186-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics