Abstract:
:A weakly nonlinear oscillator of natural frequency omega(0) and damping ratio delta is driven by an amplitude-modulated force of dimensionless amplitude epsilon, carrier frequency omega, and modulation frequency omega(1). Each of (omega - omega(0))/omega(0), omega(1)/omega(0), and delta is O(epsilon(2/3)) as epsilon --> 0. The response in this resonant neighborhood is a slowly modulated sine wave, the envelope of which is described by three first-order, autonomous, ordinary differential equations. This envelope, which is periodic for delta > epsilon(2/3), is chaotic in certain ranges of (omega - omega(0))/omega(0) and omega(1)/omega(0) if delta/epsilon(2/3) is sufficiently small.
journal_name
Proc Natl Acad Sci U S Aauthors
Miles Jdoi
10.1073/pnas.81.12.3919subject
Has Abstractpub_date
1984-06-01 00:00:00pages
3919-23issue
12eissn
0027-8424issn
1091-6490journal_volume
81pub_type
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