An Experimental Investigation of Coupled van der Pol Oscillators

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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Experimental Synchronization of Two Van der Pol Oscillators with Nonlinear and Delayed Unidirectional Coupling

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0024 ◽

2017 ◽

Vol 18 (6) ◽

pp. 515-523 ◽

Cited By ~ 2

Author(s):

Raoul Thepi Siewe ◽

Alain Francis Talla ◽

Paul Woafo

Keyword(s):

Experimental Investigation ◽

Numerical Investigation ◽

Experimental Results ◽

Coupling Coefficients ◽

Electronic Circuits ◽

Periodic Patterns ◽

Chaotic State ◽

Van Der Pol ◽

Unidirectional Coupling ◽

Van Der Pol Oscillators

AbstractThis paper presents the experimental investigation on synchronization of two Van der Pol oscillators with polynomial and delay unidirectional couplings. The intervals of coupling coefficients and delay leading to synchronization are determined experimentally using analog electronic circuits. Three cases are considered: autonomous Van der Pol oscillators, sinusoidally exited Van der Pol oscillators in the chaotic state and Van der Pol oscillators with two slowly sinusoidal excitations delivering periodic patterns of periodic pulses. It is found that the degree of the polynomial coupling reduces the intervals of coupling coefficients leading to synchronization and the delay affects the coupling intervals in a periodic way. The experimental results agree well with the results of the theoretical (mathematical and numerical) investigation.

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A Numerical Investigation of Phase-Locked and Chaotic Behavior of Coupled Van Der Pol Oscillators

Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems ◽

10.1115/detc1995-0275 ◽

1995 ◽

Author(s):

Per G. Reinhall ◽

Duane W. Storti

Keyword(s):

Parameter Space ◽

Chaotic Behavior ◽

Van Der Pol Oscillator ◽

Stable Phase ◽

Phase Lag ◽

Van Der Pol ◽

Dimensional Parameter ◽

Existence And Stability ◽

Van Der Pol Oscillators ◽

Parameter Values

Abstract This paper presents the results of numerical simulations of the dynamics of a pair of linearly coupled van der Pol oscillators. A four-dimensional parameter space (including the displacement and velocity coupling strengths and the detuning in addition to the usual non-linearity parameter of the uncoupled van der Pol oscillator) is explored. In addition to corroboration of analytical results for the existence and stability of the in-phase and out-of-phase modes, regions in the parameter space are obtained where stable phase-locked motions exist with phase differences other than 0° or 180°. The dependence of stable phase lag on parameter values is presented for representative portions of the parameter space. A region is also located where trajectories are obtained which provide the first evidence of chaotic behavior and strange at tractors in this system of unforced non-conservative oscillators.

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Fabrication and Experimental Investigation of a Novel 3D Hydrodynamic Focusing Micro Cytometric Device

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.526.242 ◽

2014 ◽

Vol 526 ◽

pp. 242-249

Author(s):

Yong Quan Wang ◽

Jing Yuan Wang ◽

Hua Ling Chen

Keyword(s):

Experimental Investigation ◽

Soft Lithography ◽

Operating Conditions ◽

Experimental Results ◽

Experimental Investigations ◽

Hydrodynamic Focusing ◽

Channel Depth ◽

Feature Parameter ◽

Micro Molding ◽

Pdms Device

This paper presents the fabrication of a novel micro-machined cytometric device, and the experimental investigations for its 3D hydrodynamic focusing performance. The proposed device is simple in structure, with the uniqueness that the depth of its microchannels is non-uniform. Using the SU-8 soft lithography containing two exposures, as well as micro-molding techniques, the PDMS device is successfully fabricated. Two kinds of experiments, i.e., the red ink fluidity observation experiments and the fluorescent optical experiments, are then performed for the device prototypes with different step heights, or channel depth differences, to explore the influence laws of the feature parameter on the devices hydrodynamic focusing behaviors. The experimental results show that the introducing of the steps can efficiently enhance the vertical focusing performance of the device. At appropriate geometry and operating conditions, good 3D hydrodynamic focusing can be obtained.

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