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A scenario for torus T2 destruction via a global bifurcation

Author

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

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.

Suggested Citation

  • 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, Elsevier, vol. 39(5), pages 2198-2210.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2198-2210
    DOI: 10.1016/j.chaos.2007.06.115
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