Fundamental threshold of chaos in some nonlinear oscillators
- Institute of Radio Astronomy, 4 Krasnoznamennaya St., 310002 Kharkov (Ukraine)
A technique for predicting chaos arising in a broad class of nonlinear oscillatory systems is proposed. It is based on the notion of running Lyapunov exponents and uses the local stability properties of trajectories for determining the {open_quote}{open_quote}safe{close_quote}{close_quote} areas in the phase space where any trajectory is regular and stable in the sense of Lyapunov. The combination of this approach with harmonic balance method permits to obtain the corresponding {open_quote}{open_quote}safe{close_quote}{close_quote} regions in the control parameter space. The borders of these regions may be considered as threshold lines delimiting the areas of possible chaotic instability. An example of the two-well Duffing oscillator demonstrates good agreement between theoretically predicted values of control parameters where chaos arises with those obtained numerically. The technique is especially effective for rather high dissipation levels when other known methods such as Melnikov{close_quote}s criterion or combination of harmonic balance with analysis of variational equations fail to provide correct results. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 401118
- Report Number(s):
- CONF-950730--
- Journal Information:
- AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 375; ISSN 0094-243X; ISSN APCPCS
- Country of Publication:
- United States
- Language:
- English
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