Title: Global bifurcation analysis of the Kukles cubic system

Authors: Valery A. Gaiko

Addresses: National Academy of Sciences of Belarus, United Institute of Informatics Problems, Surganov Str. 6, Minsk 220012, Belarus

Abstract: In this paper, we carry out the global bifurcation analysis of 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. Using our geometric approach and the Wintner-Perko termination principle, we solve the problem on the maximum number and distribution of limit cycles in this system.

Keywords: planar polynomial dynamical system; Kukles cubic system; field rotation parameter; bifurcation; limit cycle; Wintner-Perko termination principle.

DOI: 10.1504/IJDSDE.2018.096219

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.4, pp.326 - 336

Available online: 16 Nov 2018 *

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