Skip to main content

Center Bifurcation for a Two-Dimensional Piecewise Linear Map

  • Chapter
Business Cycle Dynamics

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

Access this chapter

eBook
USD 16.99
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
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Afraimovich, V.S., Shil’nikov, L.P., 1983, “Invariant two-dimensional tori, their destruction and stochasticity”, Gorkii University, Gorkii, Russia, pp. 3–26.

    Google Scholar 

  • Aronson, D.G., Chory, M.A., Hall, G.R., McGehee, R.P., 1982, “Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study”, Commun. Math. Phys. 83, pp. 303–354.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Banerjee, S., Ranjan, P., Grebogi, C, 2000, “Bifurcations in Two-Dimensional Piecewise Smooth Maps-Theory and Applications in Switching Circuits”, IEEE Trans. Circuits Syst.-I: Fund. Theory Appl. 47 No. 5, pp. 633–643.

    Article  MATH  Google Scholar 

  • Boyland, P.L., 1986, “Bifurcations of circle maps: Arnol’d tongues, instability and rotation intervals”, Commun. Math. Phys., 106, pp. 353–381.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Guckenheimer, J., Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag.

    Google Scholar 

  • Gumovski, I., Mira. C, 1980, Recurrences and Discrete Dynamical Systems. Springer-Verlag.

    Google Scholar 

  • Hao Bai-Lin, 1989, Elementary Symbolic Dynamics and Chaos in Dissipative Systems. World Scientific, Singapore.

    Google Scholar 

  • Hommes, C.H., 1991, Chaotic dynamics in economic models. Wolters-Noodhoff, Groningen.

    Google Scholar 

  • Hommes, C.H., Nusse, H., 1991, “Period three to period two bifurcations for piecewise linear models”, Journal of Economics 54(2), pp. 157–169.

    MATH  MathSciNet  Google Scholar 

  • Kuznetsov, Y., 1995, Elements of applied bifurcation theory. Springer-Verlag.

    Google Scholar 

  • Maistrenko, Y., Sushko, I., Gardini, L., 1998, “About two mechanisms of reunion of chaotic attractors”, Chaos, Solitons & Fractals, 9(8), pp. 1373–1390.

    Article  MATH  MathSciNet  Google Scholar 

  • Mira, C, Gardini, L., Barugola, A., Cathala, J.C., 1996, Chaotic dynamics in two-dimensional noninvertible maps. Singapore, World Scientific.

    Book  MATH  Google Scholar 

  • Nusse, H.E., Yorke, J.A., 1992, “Border-collision bifurcations including “period two to period three” for piecewise smooth systems”, Physica D, 57, pp. 39–57.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Sushko, I., Puu, T., Gardini, L., 2003, “The Hicksian floor-roof model for two regions linked by interregional trade”, Chaos Solitons & Fractals, 18, pp. 593–612.

    Article  MATH  MathSciNet  Google Scholar 

  • Zhusubaliyev, Z.T., Mosekilde, E., 2003, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems, Singapore, World Scientific.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sushko, I., Gardini, L. (2006). Center Bifurcation for a Two-Dimensional Piecewise Linear Map. In: Puu, T., Sushko, I. (eds) Business Cycle Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32168-3_3

Download citation

Publish with us

Policies and ethics