Global bifurcations of limit cycles in the Kukles cubic system
Dynamical Systems
2016-11-28 v1
Abstract
In this paper, using our bifurcational geometric approach, we solve the problem on the maximum number and distribution of limit cycles in the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic right-hand sides and having an anti-saddle at the origin. We also apply alternatively the Wintner-Perko termination principle to solve this problem.
Keywords
Cite
@article{arxiv.1611.08113,
title = {Global bifurcations of limit cycles in the Kukles cubic system},
author = {Valery A. Gaiko},
journal= {arXiv preprint arXiv:1611.08113},
year = {2016}
}
Comments
14 pages. arXiv admin note: substantial text overlap with arXiv:math/0611142, arXiv:math/0611143, arXiv:0803.3055, arXiv:1202.3540