Intermittency and Transport Barriers in Fluids and Plasmas

  • Emanuel V. Chimanski
  • Caroline G. L. Martins
  • Roman Chertovskih
  • Erico L. RempelEmail author
  • Marisa Roberto
  • Iberê L. Caldas
  • Abraham C.-L. Chian
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 22)


Leaking chaotic systems represent physical situations in which a hole or leak is introduced in a closed chaotic system. When such a hole is present, trajectories can escape from a trapping region of the phase space and wander for some time, before they return to the first region or settle to a different attractor. In the first case, the system displays intermittency, whereas in the second case, transient chaos is observed. The presence of transport barriers can prevent the leaking of trajectories between regions of the phase space. In the present study, transport barriers and intermittency are investigated in two dynamical systems. First, the topology of the phase space for symplectic maps is analyzed when a control parameter is varied, where a robust torus may or not be present. The patterns obtained are compared and the effect of the robust torus on the dynamical transport is described. In a second example, Raleigh-Bénard convection is studied in three-dimensional direct numerical simulations. By varying the magnitude of the Rayleigh number, a route to hyperchaos is reported, where an interior crisis leads to intermittency between quasiperiodic and hyperchaotic states.



EVC, RC, and ELR acknowledge the financial support from FAPESP (grants 2016/07398-8, 2013/01242-8, and 2013/26258-4, respectively). ELR also acknowledges, financial support from CNPq (grant 305540/2014-9) and CAPES (grant 88881.068051/2014-01). RC was also partially supported by the project POCI-01-0145-FEDER-006933/SYSTEC financed by ERDF (European Regional Development Fund) through COMPETE 2020 (Programa Operacional Competitividade e Internacionalização), and by FCT (Fundação para a Ciência e a Tecnologia, Portugal).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Emanuel V. Chimanski
    • 1
  • Caroline G. L. Martins
    • 1
  • Roman Chertovskih
    • 2
    • 3
  • Erico L. Rempel
    • 4
    • 5
    Email author
  • Marisa Roberto
    • 1
  • Iberê L. Caldas
    • 6
  • Abraham C.-L. Chian
    • 7
  1. 1.Instituto Tecnológico de AeronáuticaSão José dos CamposBrazil
  2. 2.Research Center for Systems and Technologies, Faculty of EngineeringUniversity of PortoPortoPortugal
  3. 3.Samara National Research UniversitySamaraRussian Federation
  4. 4.Instituto Tecnológico de AeronáuticaSão José dos CamposBrazil
  5. 5.National Institute for Space ResearchSão José dos CamposBrazil
  6. 6.Instituto de FísicaUniversidade de São PauloSão PauloBrazil
  7. 7.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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