Bifurcation Phenomena in a Two-Degrees-of-Freedom Duffing's Equation

Hiroyuki NAKAJIMA; Yoshisuke UEDA

Bifurcation Phenomena in a Two-Degrees-of-Freedom Duffing's Equation

Hiroyuki NAKAJIMA, Yoshisuke UEDA

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This paper demonstrates results of a numerical experiment on bifurcation phenomena in a two-degrees-of-freedom Duffing's type forced oscillatory system. The regions in the parameter plane (amplitude B and angular frequency ν of the external force) are given, in which various phenomena; chaos, hyperchaos, Hopf-bifurcations, doubling of torus, crisis and windows are observed. Existence of chaos and hyperchaos is confirmed by calculating the Lyapunov exponents. Bifurcations from invariant closed curves to chaotic attractors are also considered. For this system, two types of bifurcations from invariant closed curves to chaotic attractors through doubling of torus are observed; in one case, the doubling is interrupted by modelocking, then a chaotic attractor appears suddenly, in another case, the doubling seems to continue infinitely.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1414-1419

Publication Date: 1991/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)

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Hiroyuki NAKAJIMA
Yoshisuke UEDA

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Hiroyuki NAKAJIMA, Yoshisuke UEDA, "Bifurcation Phenomena in a Two-Degrees-of-Freedom Duffing's Equation" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 6, pp. 1414-1419, June 1991, doi: .
Abstract: This paper demonstrates results of a numerical experiment on bifurcation phenomena in a two-degrees-of-freedom Duffing's type forced oscillatory system. The regions in the parameter plane (amplitude B and angular frequency ν of the external force) are given, in which various phenomena; chaos, hyperchaos, Hopf-bifurcations, doubling of torus, crisis and windows are observed. Existence of chaos and hyperchaos is confirmed by calculating the Lyapunov exponents. Bifurcations from invariant closed curves to chaotic attractors are also considered. For this system, two types of bifurcations from invariant closed curves to chaotic attractors through doubling of torus are observed; in one case, the doubling is interrupted by modelocking, then a chaotic attractor appears suddenly, in another case, the doubling seems to continue infinitely.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1414/_p

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@ARTICLE{e74-a_6_1414,
author={Hiroyuki NAKAJIMA, Yoshisuke UEDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Bifurcation Phenomena in a Two-Degrees-of-Freedom Duffing's Equation},
year={1991},
volume={E74-A},
number={6},
pages={1414-1419},
abstract={This paper demonstrates results of a numerical experiment on bifurcation phenomena in a two-degrees-of-freedom Duffing's type forced oscillatory system. The regions in the parameter plane (amplitude B and angular frequency ν of the external force) are given, in which various phenomena; chaos, hyperchaos, Hopf-bifurcations, doubling of torus, crisis and windows are observed. Existence of chaos and hyperchaos is confirmed by calculating the Lyapunov exponents. Bifurcations from invariant closed curves to chaotic attractors are also considered. For this system, two types of bifurcations from invariant closed curves to chaotic attractors through doubling of torus are observed; in one case, the doubling is interrupted by modelocking, then a chaotic attractor appears suddenly, in another case, the doubling seems to continue infinitely.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Bifurcation Phenomena in a Two-Degrees-of-Freedom Duffing's Equation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1414
EP - 1419
AU - Hiroyuki NAKAJIMA
AU - Yoshisuke UEDA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - This paper demonstrates results of a numerical experiment on bifurcation phenomena in a two-degrees-of-freedom Duffing's type forced oscillatory system. The regions in the parameter plane (amplitude B and angular frequency ν of the external force) are given, in which various phenomena; chaos, hyperchaos, Hopf-bifurcations, doubling of torus, crisis and windows are observed. Existence of chaos and hyperchaos is confirmed by calculating the Lyapunov exponents. Bifurcations from invariant closed curves to chaotic attractors are also considered. For this system, two types of bifurcations from invariant closed curves to chaotic attractors through doubling of torus are observed; in one case, the doubling is interrupted by modelocking, then a chaotic attractor appears suddenly, in another case, the doubling seems to continue infinitely.
ER -