Coexistence of limit cycles and invariant algebraic curves for a Kukles system

DOI10.1016/j.na.2004.07.028zbMath1076.34029OpenAlexW2045856835MaRDI QIDQ1763683

Ivan Szanto, Maite Grau, Javier Chavarriga, Eduardo Sáez

Publication date: 22 February 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.07.028

zbMATH Keywords

limit cyclesinvariant algebraic curvesKukles system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (14)

Coexistence of algebraic and nonalgebraic limit cycles in Kukles systems ⋮ On the limit cycles of a class of Kukles type differential systems ⋮ Limit cycles in Kukles systems of arbitrary degree with invariant ellipse ⋮ Uniqueness of limit cycles bounded by two invariant parabolas. ⋮ Limit cycles for generalized Kukles polynomial differential systems ⋮ Maximum number of limit cycles for generalized Kukles differential system ⋮ On the cubic Kukles systems with an algebraic limit cycle of degree two ⋮ On the limit cycles of a class of generalized Kukles polynomial differential systems via averaging theory ⋮ Limit cycles and invariant curves in a class of switching systems with degree four ⋮ Bifurcations of limit cycles in Kukles systems of arbitrary degree with invariant ellipse ⋮ Maximum number of limit cycles for generalized Kukles polynomial differential systems ⋮ Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four ⋮ Limit cycles for a class of discontinuous piecewise generalized kukles differential systems ⋮ ON THE LIMIT CYCLES FOR A CLASS OF GENERALIZED KUKLES DIFFERENTIAL SYSTEMS

Cites Work

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• A method of constructing cycles without contact around a weak focus
• Conditions for the existence of a center for the Kukles homogeneous systems
• More results on the bifurcation of limit cycles for systems of Liénard type
• On the conditions of Kukles for the existence of a Centre
• On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
• The number of limit cycles of certain polynomial differential equations
• Local Bifurcations of Critical Periods in the Reduced Kukles System
• On a Result of Darboux
• Invariant algebraic curves and rational first integrals for planar polynomial vector fields

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