On the limit cycles of a class of generalized Kukles polynomial differential systems via averaging theory

DOI10.1155/2015/325102zbMath1332.34069OpenAlexW2006652335WikidataQ59106908 ScholiaQ59106908MaRDI QIDQ499828

Amar Makhlouf, Amor Menaceur

Publication date: 6 October 2015

Published in: International Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2015/325102

zbMATH Keywords

limit cycleaveraging methodgeneralized Kukles systembifurcation, center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (1)

Maximum number of limit cycles for generalized Kukles differential system

Cites Work

• Limit cycles for the kukles system
• Limit cycles for generalized Kukles polynomial differential systems
• Averaging methods for finding periodic orbits via Brouwer degree.
• Coexistence of limit cycles and invariant algebraic curves for a Kukles system
• Cubic systems of nonlinear oscillations with seven limit cycles
• On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
• Local Bifurcations of Critical Periods in the Reduced Kukles System
• The centres in the reduced Kukles system
• Averaging methods in nonlinear dynamical systems
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