Seven Limit Cycles Around a Focus Point in a Simple Three-Dimensional Quadratic Vector Field

DOI10.1142/S0218127414500837zbMath1296.34101MaRDI QIDQ3191239

Yun Tian, Pei Yu

Publication date: 1 October 2014

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

zbMATH Keywords

limit cycleHopf bifurcationnormal formcenter manifoldMaplefocus valuethree-dimensional quadratic vector field

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Invariant manifolds for ordinary differential equations (34C45)

Related Items (9)

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry ⋮ Weak Bi-Center and Bifurcation of Critical Periods in a Three-Dimensional Symmetric Quadratic System ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for a class of cubic Kolmogorov systems in \(\mathbb{R}^3\) ⋮ Nine limit cycles around a weak focus in a class of three-dimensional cubic Kukles systems ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for four‐dimensional systems ⋮ Bifurcation analysis on a class of three-dimensional quadratic systems with twelve limit cycles ⋮ A Class of Three-Dimensional Quadratic Systems with Ten Limit Cycles ⋮ Identifying weak focus and center in a convection model ⋮ Ten limit cycles around a center-type singular point in a 3-d quadratic system with quadratic perturbation

Uses Software

• Maple

Cites Work

• Unnamed Item
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• AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES
• A Cubic System with Eight Small-Amplitude Limit Cycles
• FOUR LIMIT CYCLES FROM PERTURBING QUADRATIC INTEGRABLE SYSTEMS BY QUADRATIC POLYNOMIALS
• On hereditarily indecomposable Banach spaces

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