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Research Papers

An Experimental Investigation of Coupled van der Pol Oscillators

[+] Author and Article Information
Bhaskar Choubey1

Department of Electronics and Electical Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, UKbhaskar@elec.gla.ac.uk

1

Corresponding author.

J. Vib. Acoust 132(3), 031013 (May 13, 2010) (8 pages) doi:10.1115/1.4000808 History: Received June 22, 2009; Revised September 23, 2009; Published May 13, 2010; Online May 13, 2010

Experimental investigations of synchronization of linearly diffusive coupled van der Pol electronic oscillators are reported. In addition to in- and antiphase stable oscillations, shifted symmetric and asymmetric trajectories have been observed experimentally. However, the experiments have failed to produce stable chaotic behavior in these systems. Extended numeric simulations are then performed to show that the previously believed chaotic region is a transient numeric effect, thereby validating experimental results.

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Figures

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Figure 1

Response of coupled Van der Pol oscillators showing shifted asymmetric trajectory at ϵ=10, ϵB=−2.5, and ϵA=1.75

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Figure 2

Response of coupled Van der Pol oscillators showing shifted symmetric trajectory at ϵ=10, ϵB=−2.5, and ϵA=2.8

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Figure 3

Response of coupled Van der Pol oscillators showing the presence of chaos at ϵ=10, ϵB=−2.5, and ϵA=2.033

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Figure 4

Schematic of a van der Pol oscillator

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Figure 5

Schematic of the coupling block

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Figure 6

Oscilloscope trace of the response of the two oscillators in phase at ϵ=10, ϵB=−0.5, and ϵA=2

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Figure 7

Oscilloscope trace of the response of the two oscillators in anti-phase at ϵ=10, ϵB=−4.5, and ϵA=2

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Figure 8

Oscilloscope trace of the response of oscillators showing shifted asymmetric trajectory at ϵ=10, ϵB=−2.537, and ϵA=1.9

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Figure 9

Shifted symmetric trajectory as observed on the oscilloscope at ϵ=10, ϵB=−2.537, and ϵA=3.9

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Figure 10

Oscilloscope trace of the response of the two oscillators showing stable oscillations at ϵ=10, ϵB=−2.537, and ϵA=2.031

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Figure 11

Oscilloscope trace of the response of the two oscillators showing chaos like response at ϵ=10, ϵB=−2.51, and ϵA=2.01

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Figure 12

Extended numeric time history of the believed chaotic regime with stable anti-phase oscillations at ϵ=10, ϵB=−2.5, and ϵA=2.033

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Figure 13

Extended numeric time history of the believed chaotic regime showing transition into stable oscillation at ϵ=10, ϵB=−2.5, and ϵA=2.033

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