Weak centers and local bifurcation of critical periods in a \(Z_2\)-equivariant vector field of degree 5

DOI10.1142/s0218127423500293zbMATH Open1544.37044MaRDI QIDQ6537647

Yusen Wu, Feng Li

Publication date: 14 May 2024

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

zbMATH Keywords

weak centercritical period bifurcation\(Z_2\)-equivariant vector field of degree 5complex period constant

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40)

Cites Work

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• Complete study on a bi-center problem for the \(Z_2\)-equivariant cubic vector fields
• Weak center problem and bifurcation of critical periods for a \(Z_4\)-equivariant cubic system
• Integrability and linearizability of cubic \(Z_2\) systems with non-resonant singular points
• Decomposition of algebraic sets and applications to weak centers of cubic systems
• Bifurcation of critical periods from the rigid quadratic isochronous vector field
• On the number of critical periods for planar polynomial systems
• On the number of critical points of the period
• Mechanical manipulation for a class of differential systems
• The centre conditions for a certain cubic system
• A new method to determine isochronous center conditions for polynomial differential systems.
• Weak centers and bifurcation of critical periods in reversible cubic systems
• Centers and isochronous centers of a class of quasi-analytic switching systems
• Isochronicity of a \(\mathbb{Z}_2\)-equivariant quintic system
• Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields
• On the critical periods of Liénard systems with cubic restoring forces
• Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points
• Global bifurcation studies of a cubic Liénard system
• Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems
• Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems
• CRITICAL PERIODS OF PLANAR REVERTIBLE VECTOR FIELD WITH THIRD-DEGREE POLYNOMIAL FUNCTIONS
• The Center and Cyclicity Problems
• Bifurcation of Critical Periods for Plane Vector Fields
• Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• Local Bifurcations of Critical Periods in the Reduced Kukles System
• Centennial History of Hilbert's 16th Problem
• Simultaneity of centres in ℤ _q -equivariant systems
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• GLOBAL BIFURCATION OF LIMIT CYCLES IN A FAMILY OF MULTIPARAMETER SYSTEM
• Critical period bifurcations of a cubic system
• CRITICAL PERIODS OF THIRD-ORDER PLANAR HAMILTONIAN SYSTEMS
• Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System
• LOCAL AND GLOBAL BIFURCATIONS TO LIMIT CYCLES IN A CLASS OF LIÉNARD EQUATION

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