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TECHNICAL PAPERS

An Investigation of Coupled van der Pol Oscillators

[+] Author and Article Information
Lesley Ann Low, Per G. Reinhall, Duane W. Storti

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195

J. Vib. Acoust 125(2), 162-169 (Apr 01, 2003) (8 pages) doi:10.1115/1.1553469 History: Received September 01, 2000; Revised September 01, 2002; Online April 01, 2003
Copyright © 2003 by ASME
Topics: Stability , Motion , Equations
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References

Figures

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Transition curve, ε=2.5. (Response at Pts. A,B and C shown in Figs. 3, 4 and 10)
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Transition curves, ε=0.5, 2.5, 5, 7.5 and 10. (ε=0.5 on top and ε=10 on bottom)
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In-phase response (Pt. A on Fig. 1), ε=2.5,εA=3.0,εB=−0.4
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Out-of-phase response (Pt. B on Fig. 1), ε=2.5,εA=2.0,εB=−1.4
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Shifted asymmetric trajectory (ε=10,εB=−2.5,εA=1.765)
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Shifted symmetric trajectory (ε=10,εB=−2.5,εA=2.75)
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Transition curve, ε=10, with shifted symmetric (rightmost region with thick outline), and shifted asymmetric regions (leftmost region with thick outline)
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Transition curve, ε=10.0 (upper left), 7.5 (upper right), 5.0 (lower left), 2.5 (lower right) with shifted symmetric (rightmost region with thick outline), and shifted asymmetric regions (leftmost region with thick outline)
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Phase lag (ϕ) versus εB(ε=10,εA=0.3)
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Time history of chaotic regime (ε=10,εB=−2.5,εA=2.033)
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Bifurcation plot, x,y amplitude per cycle versus εA(ε=10 and εB=−2.5)
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Correlation dimension (ε=10,B=−2.5,A=2.033)
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Poincare map (ε=10,B=−2.5,A=2.033)
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Transition curves, ε=1(εΔ=0.5,εΔ=0.25,εΔ=0)
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Transition curve, ε=1(εΔ=0.25 and εΔ=0)
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Transition curve, ε=1(εΔ=0.5 and εΔ=0)
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Time history, beating (T=50 sec), no phase-locking region with detuning (εΔ=0.25,ε=1,εA=0.4912,εB=0.0004)
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Transition curves (analytical results) for the network of 2, 3, 4, 5 and 6 coupled van der Pol oscillators, ε=1.0
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Analytical (line) and numerical (points) transition curves of 3 and 4 coupled van der Pol oscillators, ε=1.0

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