Skip to main content

Numerical Simulation for the Hopf Bifurcation in TCP Systems

  • Conference paper
  • First Online:
Proceedings of the European Computing Conference

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 27))

  • 708 Accesses

Abstract

In this paper, an Internet model with one route, one resource, and a nonadaptive user and round-trip continuous distributed delay has been studied. We have shown that a Hopf bifurcation occurs in such a model, yielding a family of periodic orbits bifurcating out from the network equilibrium. A simulation is given to verify 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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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. Hassard BD, Kazarinoff ND, Wan YH (1981) Theory and applications of Hopf bifurcation. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  2. Kelly FP (2000) Models for a self-managed internet. Philos Trans Roy Soc A 358:2335–2348

    Article  MATH  Google Scholar 

  3. Li C, Chen G, Liao X, Yu J (2004) Hopf bifurcation in an internet congestion control model. Chaos Soliton Fract 19:853–862

    Article  MATH  MathSciNet  Google Scholar 

  4. Mircea G, Neamtu M, Opris D (2003) Dynamical systems in economics, mechanics, biology described by differential equations with time delay. Mirton Publishing House, Timisoara

    Google Scholar 

  5. Mircea G, Neamtu M, Opris D (2004) Hopf bifurcations for dynamical systems with time delay and application. Mirton Publishing House, Timisoara

    Google Scholar 

  6. Mircea G, Neamtu M, Opris D (2004) Systems of harmonic oscillators with time delay and applications. In: 5th international conference on nonlinear problems in aviation and aerospace ICNPAA 2004. Cambridge Scientific Publishers Ltd., proceedings of ICNPAA 2004, pp 475–485

    Google Scholar 

  7. Mircea G, Opris D (2004) Nonlinear effects in a discrete-delay dynamic model for a stock market. In: 8th international congress on insurance: mathematics and economics, Rome, pp 506–517

    Google Scholar 

  8. Mircea G, Muntean M (2004) Nonlinear analysis of network traffic. In: The Central and East European conference on business information systems 2004, Cluj-Napoca, Risoprint Publishing House, pp 587–602

    Google Scholar 

  9. Voicu M, Mircea G (2005) Algorithms for exploiting multidimensional databases. WSEAS Trans Inf Sci Appl 2(12):2176–2183

    Google Scholar 

Download references

Acknowledgment

Results paper within the research project CEEX P-CD, code CEEX-M1-C2–505/2006–2008.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gabriela Mircea .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this paper

Cite this paper

Mircea, G., Muntean, M. (2009). Numerical Simulation for the Hopf Bifurcation in TCP Systems. In: Mastorakis, N., Mladenov, V., Kontargyri, V. (eds) Proceedings of the European Computing Conference. Lecture Notes in Electrical Engineering, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-84814-3_56

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-84814-3_56

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-84813-6

  • Online ISBN: 978-0-387-84814-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics