Bifurcations of Limit Cycles in a Class of Quartic Planar Vector Fields
Year: 2025
Type: article
Abstract: This paper studies the number and the distribution of limit cycles of a class of planar quartic vector fields $ \dot{x}=-y(ay^2-1)+\varepsilon p(x, y),\; \; \dot{y}=x(ax^2-\sqrt{a}x-1)+\varepsilon q(x, y), $ where $ a>0 $, $ 0<\varepsilon\ll 1 $, $ p(x,y) $ and $ q(x,y) $ are polynomials in $ (x,y) $ of the degree $ 4 $. By the bifurcation theory and qualitative analysis, we obtain four new configurations of limit cycles, two of which can have at least $ 12 $ limit cycles.
DOI: 10.11948/20240470
Authors: Yuan Chang, Liqin Zhao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411533651