Realizability of the normal form for the triple-zero nilpotency in a class of delayed nonlinear oscillators
Dynamical Systems
2012-05-24 v1
Abstract
The effects of delayed feedback terms on nonlinear oscillators has been extensively studied, and have important applications in many areas of science and engineering. We study a particular class of second-order delay-differential equations near a point of triple-zero nilpotent bifurcation. Using center manifold and normal form reduction, we show that the three-dimensional nonlinear normal form for the triple-zero bifurcation can be fully realized at any given order for appropriate choices of nonlinearities in the original delay-differential equation.
Keywords
Cite
@article{arxiv.1205.5045,
title = {Realizability of the normal form for the triple-zero nilpotency in a class of delayed nonlinear oscillators},
author = {Victor G. LeBlanc},
journal= {arXiv preprint arXiv:1205.5045},
year = {2012}
}
Comments
arXiv admin note: text overlap with arXiv:math/0505392