2008/03/20 by Valery A. Gaiko, Gaiko, Valery A.
Mathematics · #34C05 #34C07 #34C23 #37G05 #37G10 #37G15 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS #msc:34C05 #msc:34C07 #msc:34C23 #msc:37G05 #msc:37G10 #msc:37G15
paper · pdf · doi:10.48550/arxiv.0803.3055
10 pages
arxiv created 2008/03/20 · openalex publication_date 2008/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a quadratic system with two parallel straight line-isoclines is considered. This system corresponds to the system of class II in the classification of Ye Yanqian. Using the field rotation parameters of the constructed canonical system and geometric properties of the spirals filling the interior and exterior domains of its limit cycles, we prove that the maximum number of limit cycles in a quadratic system with two parallel straight line-isoclines and two finite singular points is equal to two. Besides, we obtain the same result in a different way: applying the Wintner-Perko termination principle for multiple limit cycles and using the methods of global bifurcation theory developed earlier by the author.