A Scenario for torus T2 destruction via a global bifurcation

T. Pereira , M. S. Baptista, M. B. Reyes , I. L. Caldas, J. C. Sartorelli , J. Kurths

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We show a scenario of a two-frequency torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T2 with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-II intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws.
Original languageEnglish
Pages (from-to)2198-2210
Number of pages13
JournalChaos, Solitons & Fractals
Volume39
Issue number5
Early online date22 Aug 2007
DOIs
Publication statusPublished - 15 Mar 2009

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Global Bifurcation
Saddle
Torus
Saddlepoint
Scenarios
Collision
Global Dynamics
Invariant Manifolds
Intermittency
Scaling Laws
Lyapunov Exponent
Breakdown
Chaos
Orbit

Cite this

Pereira , T., Baptista, M. S., Reyes , M. B., Caldas, I. L., Sartorelli , J. C., & Kurths, J. (2009). A Scenario for torus T2 destruction via a global bifurcation. Chaos, Solitons & Fractals, 39(5), 2198-2210. https://doi.org/doi:10.1016/j.chaos.2007.06.115

A Scenario for torus T2 destruction via a global bifurcation. / Pereira , T.; Baptista, M. S.; Reyes , M. B. ; Caldas, I. L. ; Sartorelli , J. C. ; Kurths, J. .

In: Chaos, Solitons & Fractals, Vol. 39, No. 5, 15.03.2009, p. 2198-2210.

Research output: Contribution to journalArticle

Pereira , T, Baptista, MS, Reyes , MB, Caldas, IL, Sartorelli , JC & Kurths, J 2009, 'A Scenario for torus T2 destruction via a global bifurcation' Chaos, Solitons & Fractals, vol. 39, no. 5, pp. 2198-2210. https://doi.org/doi:10.1016/j.chaos.2007.06.115
Pereira , T. ; Baptista, M. S. ; Reyes , M. B. ; Caldas, I. L. ; Sartorelli , J. C. ; Kurths, J. . / A Scenario for torus T2 destruction via a global bifurcation. In: Chaos, Solitons & Fractals. 2009 ; Vol. 39, No. 5. pp. 2198-2210.
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