Skip to main content
SpringerLink
Log in

Alternating Smooth and Nonsmooth Bifurcations in a Discontinuous Linear-Power Map

  • Conference paper
  • First Online:
Extended Abstracts Spring 2016

Part of the book series: Trends in Mathematics ((RPCRMB,volume 8))

  • 653 Accesses

Abstract

We study the dynamics of a one dimensional discontinuous linear-power map. It has a vertical asymptote giving rise to new kinds of border collision bifurcations. We explain the peculiar periods of attracting cycles, appearing due to cascades of alternating smooth and nonsmooth bifurcations. Robust unbounded chaotic attractors are also described.

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

Access this chapter

Log in via an institution
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. M. di Bernardo, C.J. Budd, A.R. Champneys, P. Kowalczyk, Piecewise-Smooth Dynamical Systems: Theory and Applications, vol. 163, Applied Mathematical Sciences (Springer, London, 2008)

    MATH  Google Scholar 

  2. L. Gardini, R. Makrooni, I. Sushko, Cascades of alternating smooth bifurcations and border collision bifurcations in a family of discontinuous linear-power maps, Geocomplexity Discussion Paper No.3/2016, ISSN:2409-7497, http://econpapers.repec.org/paper/cstwpaper/

  3. R. Makrooni, F. Khellat, L. Gardini, Border collision and fold bifurcations in a family of piecesiwe smooth maps. Unbounded chaotic sets (2015)

    Google Scholar 

  4. R. Makrooni, F. Khellat, L. Gardini, Border collision and fold bifurcations in a family of piecesiwe smooth maps. Divergence but not only (2015)

    Google Scholar 

  5. A.B. Nordmark, Non-periodic motion caused by grazing incidence in an impact oscillator. J. Sound Vib. 145, 279–297 (1991)

    Article  Google Scholar 

  6. A.B. Nordmark, Universal limit mapping in grazing bifurcations. Phys. Rev. E 55, 266–270 (1997)

    Article  Google Scholar 

  7. I. Sushko, V. Avrutin, L. Gardini, Bifurcation structure in the skew tent map and its application as a border collision normal form. J. Diff. Equ. Appl. (2015)

    Google Scholar 

Download references

Acknowledgements

L. Gardini acknowledges the National Group of Mathematical Physics, INDAM Italian Research Group.

Author information

Authors and Affiliations

  1. Dept. of Economics, Society, Politics (DESP), University of Urbino Carlo Bo, Via A. Saffi n.42, 61029, Urbino, Italy

    Laura Gardini

  2. Faculty of Mathematical Sciences, Shahid Beheshti University, 19839, Evin, Tehran, Iran

    Roya Makrooni

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska st. 3, Kyiv, 01601, Ukraine

    Iryna Sushko

Authors
  1. Laura Gardini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roya Makrooni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Iryna Sushko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laura Gardini .

Editor information

Editors and Affiliations

  1. DEIB, Politecnico di Milano , Milano, Italy

    Alessandro Colombo

  2. Department of Engineering Mathematics, University of Bristol , BRISTOL, Avon, United Kingdom

    Mike Jeffrey

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya , Barcelona, Spain

    J. Tomàs Lázaro

  4. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep M. Olm

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Gardini, L., Makrooni, R., Sushko, I. (2017). Alternating Smooth and Nonsmooth Bifurcations in a Discontinuous Linear-Power Map. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_11

Download citation

Publish with us

Policies and ethics

Search

Navigation