Experimental Observation of the Large-Amplitude Solutions of Duffing's and Related Equations

Experiments with a nonlinear electronic model show that certain simple features of the solutions of τ2u¯+ητu˙+f(u)=Usinωt, where f(u) is an odd monotonic function of u for example u3, repeat in a regular pattern as either τ is decreased or U is increased. For fixed U, the position of these features...

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Bibliographic Details
Published in:IMA journal of applied mathematics 1989, Vol.42 (2), p.177-201
Main Author: ROBINSON, F. N. H
Format: Article
Language:English
Subjects:
Applied sciences
Electric, optical and optoelectronic circuits
Electronics
Exact sciences and technology
Theoretical study. Circuits analysis and design
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Summary:Experiments with a nonlinear electronic model show that certain simple features of the solutions of τ2u¯+ητu˙+f(u)=Usinωt, where f(u) is an odd monotonic function of u for example u3, repeat in a regular pattern as either τ is decreased or U is increased. For fixed U, the position of these features is periodic in 1/ωτ and, when f(u) has the form u∣u∣k−1 a quantitative relation between the period in 1/ωτ and U can be found. The occurrence of large-amplitude chaotic solutions is found to depend not only on the nonlinearity of f(u) for large U but also on its behaviour near u = 0. For the Duffing equation, which can be reduced to x¯+δx˙+x3=Fsint, the range of parameters accessible to experiment is 0
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/42.2.177