Dynamics of the two-frequency torus breakdown in the driven double scroll circuit

M S Baptista, I L Caldas

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

In work we numerically identify three scenarios for the two-frequency torus breakdown to chaos, using the driven double scroll circuit, with varying driving parameters. Two of these scenarios follow the Curry-Yorke route to chaos. For one scenario, we identify the transition to chaos through the onset of a heteroclinic tangle and its heteroclinic points. In the other scenario, chaos appears via period-doubling bifurcations. The third scenario is through the type-II intermittency for which a quasiperiodic torus grows in size, breaks by touching external saddle points, and forms a heteroclinic saddle connection. These dynamic scenarios have distinct structure evolutions: for the Curry-Yorke route, chaos appears softly and alternates with phase locking, while, for the type-II intermittency, chaos appears abruptly and is pn:served for a large range of the varying driving parameter. [S1063-651X(98)05210-6].

Original languageEnglish
Pages (from-to)4413-4420
Number of pages8
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume58
Issue number4
DOIs
Publication statusPublished - Oct 1998

Keywords

  • quasi-periodicity
  • chaos
  • bifurcations
  • transition
  • turbulence
  • systems
  • onset

Cite this

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title = "Dynamics of the two-frequency torus breakdown in the driven double scroll circuit",
abstract = "In work we numerically identify three scenarios for the two-frequency torus breakdown to chaos, using the driven double scroll circuit, with varying driving parameters. Two of these scenarios follow the Curry-Yorke route to chaos. For one scenario, we identify the transition to chaos through the onset of a heteroclinic tangle and its heteroclinic points. In the other scenario, chaos appears via period-doubling bifurcations. The third scenario is through the type-II intermittency for which a quasiperiodic torus grows in size, breaks by touching external saddle points, and forms a heteroclinic saddle connection. These dynamic scenarios have distinct structure evolutions: for the Curry-Yorke route, chaos appears softly and alternates with phase locking, while, for the type-II intermittency, chaos appears abruptly and is pn:served for a large range of the varying driving parameter. [S1063-651X(98)05210-6].",
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T1 - Dynamics of the two-frequency torus breakdown in the driven double scroll circuit

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AU - Caldas, I L

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AB - In work we numerically identify three scenarios for the two-frequency torus breakdown to chaos, using the driven double scroll circuit, with varying driving parameters. Two of these scenarios follow the Curry-Yorke route to chaos. For one scenario, we identify the transition to chaos through the onset of a heteroclinic tangle and its heteroclinic points. In the other scenario, chaos appears via period-doubling bifurcations. The third scenario is through the type-II intermittency for which a quasiperiodic torus grows in size, breaks by touching external saddle points, and forms a heteroclinic saddle connection. These dynamic scenarios have distinct structure evolutions: for the Curry-Yorke route, chaos appears softly and alternates with phase locking, while, for the type-II intermittency, chaos appears abruptly and is pn:served for a large range of the varying driving parameter. [S1063-651X(98)05210-6].

KW - quasi-periodicity

KW - chaos

KW - bifurcations

KW - transition

KW - turbulence

KW - systems

KW - onset

U2 - 10.1103/PhysRevE.58.4413

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