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

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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
Issue number5
Early online date22 Aug 2007
Publication statusPublished - 15 Mar 2009

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    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