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

Hiroyuki NAKAJIMA  Yoshisuke UEDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E74-A   No.6   pp.1414-1419
Publication Date: 1991/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)

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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.