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• W1970963521 abstract "Abstract This report presents an extensive investigation of bifurcations of quasi-periodic oscillations based on an analysis of a coupled delayed logistic map. This map generates an invariant two-torus (IT 2 ) that corresponds to a three-torus in vector fields. We illustrate detailed Lyapunov diagrams and, by observing attractors, derive a quasi-periodic saddle–node (QSN) bifurcation boundary with a precision of 1 0 − 9 . We derive a stable invariant one-torus (IT 1 ) and a saddle IT 1 , which correspond to a stable two-torus and a saddle two-torus in vector fields, respectively. We confirmed that the QSN bifurcation boundary coincides with a saddle–node bifurcation point of a stable IT 1 and a saddle IT 1 . Our major concern in this study is whether the qualitative transition from an IT 1 to an IT 2 via QSN bifurcations includes phase-locking. We prove with a precision of 1 0 − 9 that there is no resonance at the bifurcation point." @default.
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• W1970963521 date "2014-12-01" @default.
• W1970963521 modified "2023-10-03" @default.
• W1970963521 title "Bifurcation boundaries of three-frequency quasi-periodic oscillations in discrete-time dynamical system" @default.
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• W1970963521 doi "https://doi.org/10.1016/j.physd.2014.09.001" @default.
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