This article is cited in 1 paper

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

T. V. Zavrazhina

International Research and Educational Center for Information Technologies and Systems, National Academy of Sciences of Ukraine, pr. Akademika Glushkova 40, Kiev, 03680, Ukraine

Abstract: 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.

Key words: dynamical system, Duffing oscillator, periodic solution on a torus, bifurcation, chaos, Everhart numerical method, Floquet theory, Feigenbaum universal constant.

UDC: 519.624.2

Received: 12.07.2005
Revised: 10.05.2007

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:10, 1622–1630

Bibliographic databases:

• 
•