Limit cycles for a variant of a generalized Riccati equation

DOI10.1016/j.aml.2016.11.016zbMath1361.34031OpenAlexW2569401912MaRDI QIDQ518476

Claudia Valls, Jaume Llibre

Publication date: 28 March 2017

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/182520

zbMATH Keywords

limit cyclesweak 16th Hilbert problemabelian integralgeneralized Riccati system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items

Maximum number of limit cycles for generalized Kukles differential system, Limit cycles of a second-order differential equation

Cites Work

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• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• On the periodic orbits of the third-order differential equation \(x^{\prime\prime\prime}-\mu x^{\prime\prime}+x^{\prime }-\mu x=\varepsilon F(x, x^{\prime },x^{\prime\prime})\)
• On the properties of a variant of the Riccati system of equations
• An Analytic Technique for the Solutions of Nonlinear Oscillators with Damping Using the Abel Equation