Quadratic perturbations of a quadratic reversible Lotka-Volterra system

DOI10.1007/S12346-010-0026-5zbMath1213.34071OpenAlexW1966709319MaRDI QIDQ611140

Jaume Llibre, Chengzhi Li

Publication date: 14 December 2010

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-010-0026-5

zbMATH Keywords

isochronous centerlimit cyclesquadratic vector fieldaveraging theory

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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) 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 (12)

Dynamics of some three-dimensional Lotka-Volterra systems ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ On the number of limit cycles bifurcating from a quartic reversible center ⋮ The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one ⋮ Quadratic double centers and their perturbations ⋮ Unnamed Item ⋮ FOUR LIMIT CYCLES FROM PERTURBING QUADRATIC INTEGRABLE SYSTEMS BY QUADRATIC POLYNOMIALS ⋮ Characterizing orbital-reversibility through normal forms ⋮ Abelian integrals and limit cycles ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ QUADRATIC PERTURBATIONS OF A CLASS OF QUADRATIC REVERSIBLE LOTKA–VOLTERRA SYSTEMS ⋮ Perturbation theory of the quadratic Lotka–Volterra double center

Cites Work

• Bifurcation of limit cycles from quadratic isochrones
• Nonlinear differential equations and dynamical systems
• Quadratic systems with center and their perturbations
• Perturbations of quadratic centers
• Averaging methods for finding periodic orbits via Brouwer degree.
• On the distribution and number of limit cycles for quadratic systems with two foci
• Averaging methods in nonlinear dynamical systems
• Unnamed Item

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