Global bifurcations of limit cycles in the Kukles cubic system

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.

14 pages. arXiv admin note: substantial text overlap with arXiv:math/0611142, arXiv:math/0611143, arXiv:0803.3055, arXiv:1202.3540