NDLI: Dynamics of Three Coupled Van der Pol Oscillators With Application to Circadian Rhythms

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Rompala, Kevin Rand, Richard Howland, Howard
Copyright Year	2005
Abstract	In this work we study a system of three van der Pol oscillators, x, y and w, coupled as follows: x¨−ε(1−x2)x˙+x=εμ(w−x)y¨−ε(1−y2)y˙+y=εμ(w−y)w¨−ε(1−w2)w˙+p2w=εμ(x−w)+εμ(y−w) Here the x and y oscillators are identical, and are not directly coupled to each other, but rather are coupled via the w oscillator. We investigate the existence of the in-phase mode x = y for ε ≪ 1. To this end we use the two variable expansion perturbation method (also known as multiple scales) to obtain a slow flow, which we then analyze using the software products MACSYMA and AUTO. Our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes. We model the circadian oscillator in each eye as a van der Pol oscillator (x and y). Although there is no direct connection between the two eyes, they are both connected to the brain, especially to the pineal gland, which is here represented by a third van der Pol oscillator (w).
Sponsorship	Design Engineering Division and Computers and Information in Engineering Division
Starting Page	1791
Ending Page	1799
Page Count	9
File Format	PDF
ISBN	0791847381
DOI	10.1115/DETC2005-84017
e-ISBN	0791837661
Volume Number	Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C
Conference Proceedings	ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Language	English
Publisher Date	2005-09-24
Publisher Place	Long Beach, California, USA
Access Restriction	Subscribed
Subject Keyword	Brain Chemistry Computer software Dynamics (mechanics) Flow (dynamics)
Content Type	Text
Resource Type	Article

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