Skip to main content
SpringerLink
Log in

Other Types of Intermittency and Some Recent Advances in the Study of Chaotic Intermittency

  • Chapter
  • First Online:
New Advances on Chaotic Intermittency and its Applications

  • 497 Accesses

Abstract

In this chapter nonclassical types of intermittency and recent advances in the study of chaotic intermittency phenomenon are described: type-V intermittency, type-X intermittency, on–off intermittency, eyelet intermittency, spatiotemporal intermittency, crisis-induced intermittency, the fine structure in intermittency, two-dimensional intermittency, horizontal visibility graphs method, multichannel reinjection, intermittency cascade, and experimental evidence of intermittency electric circuits.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and 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

References

  1. Bauer, M., Habip, S., He, D., Martiessen, W.: New type of intermittency in discontinuous maps. Phys. Rev. Lett. 68, 1625–1628 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. He, D., Bauer, M., Habip, S., Kruger, U., Martiessen, W., Christiansen, B., Wang, B.: Type V intermittency. Phys. Lett. A 171, 61–65 (1992)

    Article  Google Scholar 

  3. Fan, J., Ji, F., Guan, S., Wang, B., He, D.: The distribution of laminar lengths in type V intermittency. Phys. Lett. A 182, 232–237 (1993)

    Article  Google Scholar 

  4. Price, T., Mullin, T.: An experimental observation of a new type of intermittency. Phys. D 48, 29–52 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Platt, N., Spiegel, E., Tresser, C.: On–off intermittency: a mechanism for bursting. Phys. Rev. Lett. 70, 279–282 (1993)

    Article  Google Scholar 

  6. Heagy, J., Platt, N., Hammel, S.: Characterization of on–off intermittency. Phys. Rev. E 49, 1140–1150 (1994)

    Article  Google Scholar 

  7. Pikovsky, A., Grigory, O., Rosenblum, M., Zacks, M., Kurths, J.: Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 79, 47–50 (1997)

    Article  Google Scholar 

  8. Kurovskaya, M.: Distribution of laminar phases at eyelet-type intermittency. Tech. Phys. Lett. 34, 1063–1065 (2008)

    Article  Google Scholar 

  9. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, New York (2001)

    Book  MATH  Google Scholar 

  10. Ott, E.: Chaos in Dynamical Systems. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  11. Hramov, A., Koronovskii, A., Kurovskaya, M., Moskalenko, O.: Type-I intermittency with noise versus eyelet intermittency. Phys. Lett. A 375, 1646–1652 (2011)

    Article  MATH  Google Scholar 

  12. Boccaletti, S., Allaria, E., Meucci, R., Arecchi, F.: Experimental characterization of the transition to phase synchronization of chaotic CO 2 laser systems. Phys. Rev. Lett. 89, 194101 (2002)

    Article  Google Scholar 

  13. Lee, K., Kwak, Y., Lim, T.: Phase jumps near a phase synchronization transition in systems of two coupled chaotic oscillators. Phys. Rev. Lett. 81, 321–324 (1998)

    Article  Google Scholar 

  14. Hramov, A., Koronovskii, A., Kurovskaya, M., Boccaletti, S.: Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization. Phys. Rev. Lett. 97, 114101 (2006)

    Article  Google Scholar 

  15. White, F.: Viscous Fluid Flow. McGraw-Hill, New York (1991)

    Google Scholar 

  16. Gollubm, J.: Order and disorder in fluid motion. Proc. Natl. Acad. Sci. USA 92, 6705–6711 (1995)

    Article  Google Scholar 

  17. Lepiller, V., Prigent, A., Dumochel, F., Mutabazi, I.: Transition to turbulence in a tall annulus submitted to a radial temperature gradient. Phys. Fluids 19, 054101 (2007)

    Article  MATH  Google Scholar 

  18. Lai, Y., Tei, T.: Transient Chaos. Springer, New York (2001)

    Google Scholar 

  19. Chaté, H., Manneville, P.: Transition to turbulence via spatiotemporal intermittency. Phys. Rev. Lett. 58, 112–115 (1987)

    Article  Google Scholar 

  20. Kaneko, K.: Pattern dynamics in spatiotemporal chaos. Phys. D 34, 1–41 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  21. Qu, Z., Hu, G.: Spatiotemporal periodic states, periodic windows, and intermittency in coupled-map lattices. Phys. Rev. E 49, 1099–1108 (1994)

    Article  Google Scholar 

  22. Keeler, J., Farmer, J.: Robust space-time intermittency and 1∕f noise. Phys. D 23, 413–45 (1986)

    Article  MathSciNet  Google Scholar 

  23. Kaneko, K., Tsuda, I.: Complex System, Chaos and Beyond, a Constructive Approach with Applications in Life Sciences. Springer, Berlin (2000)

    MATH  Google Scholar 

  24. Rupp, P., Richter, R., Rehberg, I.: Critical exponents of directed percolation measured in spatiotemporal intermittency. Phys. Rev. E 67, 036209 (2003)

    Article  Google Scholar 

  25. Grebogi, C., Ott, E., Yorke, J.: Crisis, sudden changes in chaotic attractors and transient chaos. Phys. D 7, 181–200 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  26. Grebogi, C., Ott, E., Romeiras, F., Yorke, J.: Critical exponents for crisis-induced intermittency. Phys. Rev. E 36, 5365–5380 (1987)

    Article  MathSciNet  Google Scholar 

  27. Nayfeh, A., Balachandran, B.: Applied Nonlinear Dynamics. Wiley, New York (1995)

    Book  MATH  Google Scholar 

  28. de S. Cavalcante, H., Rios Leite, J.: Fine structure in scaling of type-I intermittency bifurcation. Phys. A 342, 356–362 (2004)

    Google Scholar 

  29. de S. Cavalcante, H., Rios Leite, J.: Logarithmic periodicities in the bifurcations of type-I intermittent chaos. Phys. Rev. Lett. 92, 254102 (2004)

    Google Scholar 

  30. Kim, Ch., Kye, W.: Two-dimensional intermittency. Phys. Rev. E 63, 037202 (2001)

    Article  Google Scholar 

  31. Lacasa, L., Luque, B., Ballesteros, F., Luque, J., Nuño, J.: From time series to complex networks: the visibility graph. Proc. Natl. Acad. Sci. USA 105, 4972–4975 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  32. Luque, B., Lacasa, L., Luque, J., Ballesteros, F.: Horizontal visibility graphs: exact results for random time series. Phys. Rev. E 80, 046103 (2009)

    Article  Google Scholar 

  33. Zhang, J., Small, M.: Complex network from pseudoperiodic time series: topology versus dynamics. Phys. Rev. Lett. 96, 238701 (2006)

    Article  Google Scholar 

  34. Kyriakopoulos, F., Thurner, S.: Directed network representations of discrete dynamical maps. Lect. Notes Comput. Sci. 4488, 625–632 (2007)

    Article  Google Scholar 

  35. Xu, X., Zhang, J., Small, M.: Superfamily phenomena and motifs of networks induced from time series. Proc. Natl. Acad. Sci. USA 105, 19601–19605 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Donner, R., Zou, Y., Donges, J., Marwan, N., Kurths, J.: Recurrence networks - a novel paradigm for nonlinear time series analysis. New J. Phys. 12, 033025 (2010)

    Article  Google Scholar 

  37. Donner, R., Zou, Y., Donges, J., Marwan, N., Kurths, J.: Ambiguities in recurrence-based complex network representations of time series. Phys. Rev. E 81, 015101(R) (2010)

    Google Scholar 

  38. Donner, R., Heitzig, J., Donges, J., Zou, Y., Marwan, N., Kurths, J.: The geometry of chaotic dynamics - a complex network perspective. Eur. Phys. J. 84, 653–672 (2011)

    Article  MathSciNet  Google Scholar 

  39. Campanharo, A., Sirer, M., Malmgren, D., Ramos, M., Amaral, L.: Duality between time series and networks. PLoS One 6, e23378 (2011)

    Article  Google Scholar 

  40. Gutin, G., Mansour, M., Severini, S.: A characterization of horizontal visibility graphs and combinatorics on words. Phys. A 390, 2421–2428 (2011)

    Article  MathSciNet  Google Scholar 

  41. Nuñez, A., Lacasa, L., Gomez, J., Luque, B.: Visibility algorithms: a short review. In: Zhang, Y. (ed.) New Frontiers in Graph Theory. InTech, Rijeka (2012)

    Google Scholar 

  42. Núñez, A., Lacasa, L., Gómez, J.: Horizontal visibility graphs generated by type-II intermittency. J. Phys. A Math. Theor. 47, 035102 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  43. Lacasa, L., Toral, R.: Description of stochastic and chaotic series using visibility graphs. Phys. Rev. E 82, 036120 (2010)

    Article  Google Scholar 

  44. Lacasa, L., Núñez, A., Roldán, E., Parrondo, J., Luque, B.: Time series irreversibility: a visibility graph approach. Eur. Phys. J. B 85, 217–229 (2012)

    Article  Google Scholar 

  45. Núñez, Á., Luque, B., Lacasa, L., Gómez, J., Robledo, A.: Horizontal visibility graphs generated by type-I intermittency. Phys. Rev. E 87, 052801 (2013)

    Article  Google Scholar 

  46. Schuster, H., Just, W.: Deterministic Chaos: An Introduction. Wiley VCH Verlag GmbH and Co. KGaA, Weinheim (2005)

    Book  MATH  Google Scholar 

  47. Luque, B., Lacasa, L., Robledo, A.: Feigenbaum graphs at the onset of chaos. Phys. Lett. A 376, 625–3629 (2012)

    Article  MATH  Google Scholar 

  48. Luque, B., Lacasa, L., Ballesteros, F., Robledo, A.: Feigenbaum graphs: a complex network perspective of chaos. PLoS One 6, e22411 (2011)

    Article  Google Scholar 

  49. Luque, B., Lacasa, L., Ballesteros, F., Robledo, A.: Analytical properties of horizontal visibility graphs in the Feigenbaum scenario. Chaos 22, 013109 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  50. Karamanos, K., Nicolis, G.: Symbolic dynamics and entropy analysis of Feigenbaum limit sets. Chaos Solitons Fractals 10, 1135–1150 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  51. Pikovsky, A.: A new type of intermittent transition to chaos. J. Phys. A Math. Gen. 16, L109–L112 (1983)

    Article  MathSciNet  Google Scholar 

  52. del Rio, E., Elaskar, S., Makarov, S.: Theory of intermittency applied to classical pathological cases. Chaos 23, 033112 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  53. San Martin, J., Antoranz, J.: Type-II intermittency with a double reinjection channel: multintermittency. Phys. Lett. A 219, 69–73 (1996)

    Article  Google Scholar 

  54. San Martin, J., Antoranz, J.: Type-I and type-II intermittencies with two channels of reinjection. Chaos Solitons Fractals 10, 1539–1544 (1999)

    Article  MATH  Google Scholar 

  55. Malasoma, J., Werny, P., Boiron, M.: Multichannel type-I intermittency in two models of Rayleigh-Benard convection. Chaos Solitons Fractals 15, 487–500 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  56. Letellier, C., Werny, P., Malasoma, J., Gilmore, R.: Multichannel intermittencies induced by symmetries. Phys. Rev. E 66, 036220 (2002)

    Article  Google Scholar 

  57. San Martin, J.: Intermittency cascade. Chaos Solitons Fractals 32, 816–831 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  58. San Martin, J., Rodriguez-Perez, D.: Conjugation of cascades. Chaos Solitons Fractals 39, 666–681 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  59. Hilborn, R.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford University Press, Oxford (2000)

    Book  MATH  Google Scholar 

  60. Chua, L., Lin, G.: Intermittency in a piecewise-linear circuit. IEEE Trans. Circuits Syst. 38, 510–520 (1991)

    Article  Google Scholar 

  61. Kodama, H., Sato, S., Honda, K.: Reconsideration of the renormalization-group theory on intermittent chaos. Phys. Lett. A 157, 354–356 (1991)

    Article  Google Scholar 

  62. Dubois, M., Rubio, M., Berge, P.: Experimental evidence of intermittencies associated with a subharmonic bifurcation. Phys. Rev. Lett. 51, 1446–1449 (1983)

    Article  MathSciNet  Google Scholar 

  63. Fortuna, L., Frasca, M., Xibilia, M.: Chua’s Circuit Implementations Yesterday, Today and Tomorrow. World Scientific, Singapore (2009)

    Book  Google Scholar 

  64. Stavrinides, S., Miliou, A., Laopoulos, Th., Anagnostopoulos, A.: The intermittency route to chaos of an electronic digital oscillator. Int. J. Bifurcation Chaos 18, 1561–1566 (2008)

    Article  MATH  Google Scholar 

  65. Ono, Y., Fukushima, K., Yazaki, T.: Critical behavior for the onset of type-III intermittency observed in an electronic circuit. Phys. Rev. E 52, 4520–4523 (1995)

    Article  Google Scholar 

  66. Kahn, A., Mar, D., Westervelt, R.: Spatial measurements near the instability threshold in ultrapure Ge. Phys. Rev. B 45, 8342–8347 (1992)

    Article  Google Scholar 

  67. Kim, Ch., Yim, G., Ryu, J., Park, Y.: Characteristic relations of type-III intermittency in an electronic circuit. Phys. Rev. Lett. 80, 5317–5320 (1998)

    Article  Google Scholar 

  68. del Rio, E., Velarde, M., Rodríguez-Lozano, A.: Long time data series and difficulties with the characterization of chaotic attractors: a case with intermittency III. Chaos Solitons Fractals 4, 2169–2179 (1994)

    Article  MATH  Google Scholar 

  69. Kye, W., Rim, S., Kim, Ch.: Experimental observation of characteristic relations of type-III intermittency in the presence of noise in a simple electronic circuit. Phys. Rev. E 68, 036203 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National University of Cordoba, Ciudad de Córdoba, Córdoba, Argentina

    Sergio Elaskar

  2. Polytechnic University of Madrid, Madrid, Madrid, Spain

    Ezequiel del Río

Authors
  1. Sergio Elaskar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ezequiel del Río
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Elaskar, S., del Río, E. (2017). Other Types of Intermittency and Some Recent Advances in the Study of Chaotic Intermittency. In: New Advances on Chaotic Intermittency and its Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-47837-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-47837-1_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47836-4

  • Online ISBN: 978-3-319-47837-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation