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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
