A scenario for torus T2 destruction via a global bifurcation

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

Chaos, Solitons & Fractals, 2009, vol. 39, issue 5, 2198-2210

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:39:y:2009:i:5:p:2198-2210

DOI: 10.1016/j.chaos.2007.06.115

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