On possible infinite bifurcation trees of period-3 motions to chaos in a time-delayed, twin-well Duffing oscillator View Full Text


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Article Info

DATE

2018-12

AUTHORS

Siyuan Xing, Albert C. J. Luo

ABSTRACT

In this paper, bifurcation trees of period-3 motions to chaos in a periodically forced, time-delayed, twin-well Duffing oscillator are investigated. Such period-3 motions and corresponding bifurcation trees may or may not be embedded in chaos in the bifurcation trees of period-1 motions to chaos. The bifurcation trees for period-3 motions to chaos in such a time-delayed, twin-well Duffing oscillator are obtained analytically. From the finite discrete Fourier series, harmonic frequency-amplitude characteristics for period-3 to period-6 motions are analyzed. From the analytical prediction, numerical illustrations of period-3 and period-6 motions in the time-delayed, twin-well Duffing oscillator are completed. The complexity of period-3 motions to chaos in nonlinear dynamical systems is strongly dependent on the distributions and quantity levels of harmonic amplitudes. For a very slowly varying excitation, the infinite bifurcation trees of period-3 motions to chaos can be achieved once the excitation amplitude approaches to infinity. More... »

PAGES

1429-1464

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40435-018-0418-y

DOI

http://dx.doi.org/10.1007/s40435-018-0418-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101834315


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