Periodic Solutions of Abel Differential Equations
Classical Analysis and ODEs
2007-05-23 v2 Dynamical Systems
Abstract
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.
Cite
@article{arxiv.math/0605153,
title = {Periodic Solutions of Abel Differential Equations},
author = {M. A. M. Alwash},
journal= {arXiv preprint arXiv:math/0605153},
year = {2007}
}