A Class of Three-Dimensional Quadratic Systems with Ten Limit Cycles

DOI10.1142/S0218127416501492zbMath1347.34049MaRDI QIDQ2827024

Yi-rong Liu, Wen-tao Huang, Chao-xiong Du

Publication date: 12 October 2016

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

zbMATH Keywords

limit cyclesLyapunov constantssymmetrical vector fieldsimultaneous Hopf bifurcationthree-dimensional 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)

Related Items (9)

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry ⋮ Local bifurcation and center problem for a more generalized Lorenz system ⋮ 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 ⋮ LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i>₃-EQUIVARIANT VECTOR FIELD ⋮ Isochronous solutions of a 3-dim symmetric quadratic system ⋮ Hopf bifurcation, positively invariant set, and physical realization of a new four-dimensional hyperchaotic financial system ⋮ Bifurcation analysis on a class of three-dimensional quadratic systems with twelve limit cycles

Cites Work

• The center problem on a center manifold in \(\mathbb{R}^{3}\)
• Bifurcation of limit cycles from an \(n\)-dimensional linear center inside a class of piecewise linear differential systems
• Hopf bifurcation for a class of three-dimensional nonlinear dynamic systems
• Bifurcation of limit cycles from a 4-dimensional center in \(\mathbb R^m\) in resonance \(1:N\)
• \(3\)-dimensional Hopf bifurcation via averaging theory of second order
• Ten limit cycles around a center-type singular point in a 3-d quadratic system with quadratic perturbation
• AN EXPLICIT RECURSIVE FORMULA FOR COMPUTING THE NORMAL FORM AND CENTER MANIFOLD OF GENERAL n-DIMENSIONAL DIFFERENTIAL SYSTEMS ASSOCIATED WITH HOPF BIFURCATION
• Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model
• Limit Cycles Bifurcations for a Class of Kolmogorov Model in Symmetrical Vector Field
• Seven Limit Cycles Around a Focus Point in a Simple Three-Dimensional Quadratic Vector Field

This page was built for publication: A Class of Three-Dimensional Quadratic Systems with Ten Limit Cycles