Limit cycles bifurcated from some reversible quadratic centres with a non-algebraic first integral

DOI10.1088/0951-7715/25/6/1653zbMath1250.34026OpenAlexW1998527012MaRDI QIDQ2895582

Changjian Liu

Publication date: 3 July 2012

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/25/6/1653

zbMATH Keywords

bifurcationlimit cycleAbelian integralMelnikov functionnon-algebraic first integralplanar reversible quadratic system

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (8)

On the limit cycles of planar polynomial system with non-rational first integral via averaging method at any order ⋮ The cyclicity of a class of quadratic reversible centers defining elliptic curves ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Limit Cycles Bifurcating from a Family of Reversible Quadratic Centers via Averaging Theory ⋮ Limit cycle bifurcations in perturbations of a reversible quadratic system with a non-rational first integral ⋮ Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center ⋮ New family of abelian integrals satisfying Chebyshev property ⋮ A new Chebyshev criterion and its application to planar differential systems

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