Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Eigenvalue Based Stability Analysis for Asymmetric Complex Dynamical Networks

  • Conference paper
Complex Sciences (Complex 2009)

Abstract

The problem of stabilization in complex networks with asymmetric couplings forced by pinning control is studied. By using eigenvalue analysis, controllable regions for different types of coupling links are obtained. Some relevant factors on controllability such as pinning fraction and pinning strength are also investigated.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Watts, D.J., Strogatz, S.H.: Collective Dynamics of ‘Small World’ Networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  2. Barabási, A.-L., Albert, R., Jeong, H.: Mean-Field Theory for Scale-Free Random Networks. Phys. A 272, 173–187 (1999)

    Article  Google Scholar 

  3. Albert, R., Barabási, A.-L.: Statistical Mechanics of Complex Networks. Reviews of Modern Physics 74, 47–97 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, X.F., Chen, G.: Synchronization in Scale-free Dynamical Networks: Robustness and Fragility. IEEE Trans. Circuits Syst. I 49, 54–62 (2002)

    Article  MathSciNet  Google Scholar 

  5. Newman, M.E.J.: The Structure and Function of Complex Networks. SIAM Review 45(2), 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, F., Chen, Z.Q., Yuan, Z.Z.: A realistic model for complex networks with local interaction, self-organization and order. Chinese Physics 16, 287–291 (2007)

    Article  Google Scholar 

  7. Chen, F., Chen, Z.Q., Liu, Z.X., Xiang, L.Y., Yuan, Z.Z.: Finding and evaluationg the hierarchical structure in complex networks. J. Phys. A: Math. Theor. 40, 5013 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wang, X.F., Chen, G.: Pinning Control of Scale-Free Dynamical Networks. Phys. A 310, 521–531 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, X., Wang, X.F., Chen, G.: Pinning a Complex Dynamical Network to Its Equilibrium. IEEE Trans. Circuits Syst. I 51(10), 2074–2087 (2004)

    Article  MathSciNet  Google Scholar 

  10. Tadic, B.: Dynamics of Directed Graphs: the World-Wide Web. Phys. A 293, 273–284 (2001)

    Article  MATH  Google Scholar 

  11. Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph Structure in the Web. Computer Network 33, 309 (2000)

    Article  Google Scholar 

  12. Schwartz, N., Cohen, R., Ben-Avraham, D., Barabási, A.-L., Havlin, S.: Percolation in Directed Scale-Free Networks. Phys. Rev. E 66, 015104 (2002)

    Article  MathSciNet  Google Scholar 

  13. Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random Graphs with Arbitrary Degree Distribution and Their Applications. Phys. Rev. E 64, 026118 (2001)

    Article  Google Scholar 

  14. Bapart, R.B.: Nonnegative Matrices and Applications. Cambridge University, Cambridge (1997)

    Book  Google Scholar 

  15. Lorenz, E.N.: Deterministic Nonperiodic Flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  16. Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifur. Chaos 9, 1465–1466 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

About this paper

Cite this paper

Chen, Z., Xiang, L., Liu, Z., Yuan, Z., Chang, K. (2009). Eigenvalue Based Stability Analysis for Asymmetric Complex Dynamical Networks. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02469-6_91

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02469-6_91

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02468-9

  • Online ISBN: 978-3-642-02469-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics