Preliminary analytical and numerical investigations of a van der Pol type oscillator having discontinuous dependence on the velocity

The van der Pol equation [1, 2] x+ x = epsilon(1 - x2)x, (1) where epsilon is a positive parameter, provides a model of a one-dimensional oscillatory system having a unique limit cycle. It is of interest, both mathematically and from the viewpoint of future applications to the natural and engineerin...

Full description

Saved in:
Bibliographic Details
Published in:Journal of sound and vibration 2005-01, Vol.279 (1), p.519-523
Main Authors: Mickens, R.E., Oyedeji, K., Rucker, S.A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The van der Pol equation [1, 2] x+ x = epsilon(1 - x2)x, (1) where epsilon is a positive parameter, provides a model of a one-dimensional oscillatory system having a unique limit cycle. It is of interest, both mathematically and from the viewpoint of future applications to the natural and engineering sciences, to consider generalizations of this equation. A nontrivial extension of Eq. (1) is x + x = epsilon(1 - x2), (2) where the "sign function" is defined to be, for real z, sign(z) = {+1, z > 0 0, z=0, -1, z < 0. (3) The purpose of this communication is to present the results of our preliminary investigations on Eq.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2004.01.047