Vibration of the Duffing Oscillator: Effect of Fractional Damping
Keyword(s):
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear tools as Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude μ_c, which a sufficient condition of a global homoclinic bifurcation, we have observed the region with a transient chaotic motion.
2015 ◽
Vol 25
(02)
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pp. 1550024
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2017 ◽
Vol 2017
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pp. 1-8
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2016 ◽
Vol 26
(05)
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pp. 1650085
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2019 ◽
Vol 14
(7)
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