CENTER PROBLEM FOR THIRD-ORDER ODEs

DOI10.1142/S0218127413500788zbMath1270.34045DBLPjournals/ijbc/Mahdi13OpenAlexW2002121911WikidataQ38316989 ScholiaQ38316989MaRDI QIDQ2845294

Adam Mahdi

Publication date: 22 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127413500788

zbMATH Keywords

center manifoldfirst integralcenter-focus problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Invariant manifolds for ordinary differential equations (34C45)

Related Items (9)

Rigid centres on the center manifold of tridimensional differential systems ⋮ Lower bounds for the cyclicity of centers of quadratic three-dimensional systems ⋮ Nine limit cycles around a weak focus in a class of three-dimensional cubic Kukles systems ⋮ Center problem in the center manifold for quadratic and cubic differential systems in \(\mathbb{R}^3\) ⋮ Cyclicity of rigid centres on centre manifolds of three-dimensional systems ⋮ Center problem in the center manifold for quadratic differential systems in \(\mathbb{R}^3\) ⋮ The Hopf bifurcation in the Shimizu-Morioka system ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ Symbolic computation for the qualitative theory of differential equations

Cites Work

• The center problem on a center manifold in \(\mathbb{R}^{3}\)
• Existence of inverse Jacobi multipliers around Hopf points in \(\mathbb R^3\): emphasis on the center problem
• Classification of the centers and their isochronicity for a class of polynomial differential systems of arbitrary degree
• Bifurcation of limit cycles for 3D Lotka-Volterra competitive systems
• Limit cycles and singular point quantities for a 3D Lotka-Volterra system
• A survey on the inverse integrating factor
• Localization and primary decomposition of polynomial ideals
• Centers on center manifolds in the Lü system
• Hopf bifurcation for a class of three-dimensional nonlinear dynamic systems
• Center conditions at infinity for Abel differential equations
• Gröbner bases and primary decomposition of polynomial ideals
• Quadratic systems with center and their perturbations
• A survey of quadratic systems
• Inverse Jacobi multipliers
• The focus-centre problem for a type of degenerate system

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