Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation

被引：0

作者：

Zavrazhina T.V. ^{[1
]}

机构：

[1] International Research and Educational Center for Information Technologies and Systems, National Academy of Sciences of Ukraine, Kiev 03680

来源：

Computational Mathematics and Mathematical Physics | 2007年 / 47卷 / 10期

关键词：

Bifurcation; Chaos; Duffing oscillator; Dynamical system; Everhart numerical method; Feigenbaum universal constant; Floquet theory; Periodic solution on a torus;

D O I：

10.1134/S0965542507100041

中图分类号：

学科分类号：

摘要：

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 R2. 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. © 2007 Pleiades Publishing, Ltd.

引用

页码：1622 / 1630

页数：8

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