Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes

DOI10.3934/cpaa.2010.9.583zbMath1198.34049OpenAlexW2081892360MaRDI QIDQ974362

Jiang Yu, Chengzhi Li, Iliya D. Iliev

Publication date: 27 May 2010

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2010.9.583

zbMATH Keywords

limit cyclesbifurcationcomplete elliptic integralsperiod annulus

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) 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 (11)

On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line ⋮ The cyclicity of a class of quadratic reversible system of genus one ⋮ 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 bifurcated from a class of quadratic reversible center of genus one ⋮ The cyclicity of period annuli of a class of quadratic reversible systems with two centers ⋮ The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one ⋮ Quadratic perturbations of a quadratic reversible center of genus one ⋮ On the limit cycles bifurcating from a quadratic reversible center of genus one ⋮ Abelian integrals and limit cycles ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs

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