Geodesic
Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 10, pp. 1692-1700

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A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in $\mathbb R^2$. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed. 
@article{ZVMMF_2007_47_10_a3,
     author = {T. V. Zavrazhina},
     title = {Numerical simulation of the transition to chaos in a~dissipative {Duffing} oscillator with two-frequency excitation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1692--1700},
     publisher = {mathdoc},
     volume = {47},
     number = {10},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a3/}
}
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T. V. Zavrazhina. Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 10, pp. 1692-1700. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a3/