Vibration of the Duffing Oscillator: Effect of Fractional Damping

Marek Borowiec; Grzegorz Litak; Arkadiusz Syta

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Vibration of the Duffing Oscillator: Effect of Fractional Damping

Marek Borowiec·Grzegorz Litak·Arkadiusz Syta

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Abstract

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 $\mu_c$, which is the sufficient condition of a global homoclinic bifurcation, we have observed the region with a transient chaotic motion.

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Marek Borowiec, Grzegorz Litak, Arkadiusz Syta. 2006-01-14. Vibration of the Duffing Oscillator: Effect of Fractional Damping. https://arxiv.org/abs/nlin/0601033

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