Global bifurcations of limit cycles in the Kukles cubic system

2016/11/24 by Valery A. Gaiko, Gaiko, Valery A.
Mathematics · Physics and Astronomy · Medicine · #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1611.08113

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.

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