Bifurcation analysis of four-frequency quasi-periodic oscillations in a three-coupled delayed logistic map

Shuya Hidaka, Naohiko Inaba, Munehisa Sekikawa, Tetsuro Endo

doi:10.1016/j.physleta.2014.12.022

Bifurcation analysis of four-frequency quasi-periodic oscillations in a three-coupled delayed logistic map

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書誌事項

公開日: 2015-03

権利情報

https://www.elsevier.com/tdm/userlicense/1.0/

DOI

10.1016/j.physleta.2014.12.022

公開者: Elsevier BV

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説明

Abstract We present herein an extensive analysis of the bifurcation structures of quasi-periodic oscillations generated by a three-coupled delayed logistic map. Oscillations generate an invariant three-torus, which corresponds to a four-dimensional torus in vector fields. We illustrate detailed two-parameter Lyapunov diagrams, which reveal a complex bifurcation structure called an Arnol'd resonance web. Our major concern in this study is to demonstrate that quasi-periodic saddle-node bifurcations from an invariant two-torus to an intermittent invariant three-torus occur because of a saddle-node bifurcation of a stable invariant two-torus and a saddle invariant two-torus. In addition, with some assumptions, we derive a bifurcation boundary between a stable invariant two-torus and a stable invariant three-torus due to a quasi-periodic Hopf bifurcation with a precision of 10 − 5 .