Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface

被引：10

作者：

Wang, Zhen ^{[1
]}

Wei, Zhouchao ^{[2
]}

Xi, Xiaojian ^{[1
]}

Li, Yongxin ^{[1
]}

机构：

[1] Xijing Univ, Dept Math, Xian 710123, Peoples R China

[2] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China

来源：

NONLINEAR DYNAMICS | 2014年 / 77卷 / 04期

关键词：

Invariant algebraic surface; Dynamics at infinity; Poincare compactification; Singularly degenerate heteroclinic cycle; GENERALIZED LORENZ SYSTEMS; DARBOUX POLYNOMIALS; GLOBAL DYNAMICS; CHAOTIC SYSTEM; BIFURCATION; ATTRACTOR; INFINITY; SADDLE;

D O I：

10.1007/s11071-014-1395-0

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

An invariant algebraic surface is calculated for a 3D autonomous quadratic system. Also, the dynamics near finite singularities and near infinite singularities on the invariant algebraic surface is analyzed. Furthermore, pitchfork bifurcation is analyzed using center manifold theorem and a first integral of this quadratic system for some special parameters is provided. Finally, the dynamics of this system at infinity using the Poincare compactification in is investigated and the singularly degenerate heteroclinic cycles are presented by a first integral and verified by numerical simulations.

引用

页码：1503 / 1518

页数：16

共 36 条

[1] Homoclinic connections in strongly self-excited nonlinear oscillators: The Melnikov function and the elliptic Lindstedt-Poincare method [J].