New criteria for the existence and non-existence of limit cycles in Liénard differential systems

DOI10.1080/14689360802568086zbMath1194.34049OpenAlexW2026286741MaRDI QIDQ5321910

Jaume Llibre, Armengol Gasull, Hector J. Giacomini

Publication date: 16 July 2009

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689360802568086

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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 (7)

Limit cycles of generalized Liénard polynomial differential systems via averaging theory ⋮ A survey on the inverse integrating factor ⋮ Probability of existence of limit cycles for a family of planar systems ⋮ Uniqueness and non-uniqueness of limit cycles for piecewise linear differential systems with three zones and no symmetry ⋮ Effectiveness of the Bendixson-Dulac theorem ⋮ Two limit cycles in Liénard piecewise linear differential systems ⋮ Some Applications of the Extended Bendixson-Dulac Theorem

Cites Work

• A note on existence and uniqueness of limit cycles for Liénard systems
• Liénard systems and potential-Hamiltonian decomposition. III: Applications
• Upper bounds for the number of limit cycles through linear differential equations
• Limit cycle uniqueness for a class of planar dynamical systems
• Existence of limit cycles for generalized Liénard equations
• Polynomial Liénard equations near infinity
• Quadratic Liénard equations with quadratic damping
• A new criterion for controlling the number of limit cycles of some generalized Liénard equations
• Sufficient conditions for the existence of at least \(n\) or exactly \(n\) limit cycles for the Liénard differential systems
• Some criteria for presence and absence of limit cycles in dynamical systems of the second order
• On the nonexistence, existence and uniqueness of limit cycles
• On the uniqueness and nonexistence of limit cycles for predator prey systems

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