Analysis of the fast-slow hyperchaotic Lorenz system

被引：9

作者：

Han Xiu-Jing ^{[1
]}

Jiang Bo ^{[1
]}

Bi Qin-Sheng ^{[1
]}

机构：

[1] Jiangsu Univ, Fac Sci, Zhenjiang 212013, Peoples R China

来源：

ACTA PHYSICA SINICA | 2009年 / 58卷 / 09期

基金：

中国国家自然科学基金;

关键词：

hyperchaotic Lorenz system; Hopf bifurcation; symmetric fold/subHopf bursting; slow passage effect;

D O I：

10.7498/aps.58.6006

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The stability of the origin of the hyperchaotic Lorenz system with two time scales is investigated. The characteristics of Hopf bifurcation from the origin, including the existence condition, the direction as well as the stability of bifurcating periodic solutions are discussed in detail, which can be demonstrated by the numerical simulations. With certain parameter, the fast-slow system can exhibit symmetric bursting and further lead to hyperchaotic movement. Based on the method of slow-fast analysis, different bifurcation forms between quiescent state and spiking has been revealed and the influence of coupling strength on slow passage effect is disscussed.

引用

页码：6006 / 6015

页数：10

共 22 条

[1]

[Anonymous], INT J CIRC THEORY AP

[2]

[Anonymous], 2012, Weakly connected neural networks

[3] THE SLOW PASSAGE THROUGH A HOPF-BIFURCATION - DELAY, MEMORY EFFECTS, AND RESONANCE [J].

BAER, SM ;

ERNEUX, T ;

RINZEL, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1989, 49 (01) :55-71

[4] New 3D-scroll attractors in hyperchaotic Chua's circuits forming a ring [J].

Cafagna, D ;

Grassi, G .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (10) :2889-2903

[5] Analysis and circuit implementation of a new four-dimensional non-autonomous hyper-chaotic system [J].

Cang Shi-Jian ;

Chen Zeng-Qiang ;

Yuan Zhu-Zhi .

ACTA PHYSICA SINICA, 2008, 57 (03) :1493-1501

[6]

Chen G., 1998, From Chaos to Order-Methodologies, Perspective and Applications, P12

[7] Hyperchaos generated from Chen's system [J].

Gao, Tiegang ;

Chen, Zengqiang ;

Yuan, Zhuzhi ;

Chen, Guanrong .

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2006, 17 (04) :471-478

[8]

Guckenheimer J., 2013, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

[9]

Hassard BD, 1981, THEORY APPL HOPF BIF

[10] UNDERSTANDING BURSTING OSCILLATIONS AS PERIODIC SLOW PASSAGES THROUGH BIFURCATION AND LIMIT POINTS [J].

HOLDEN, L ;

ERNEUX, T .

JOURNAL OF MATHEMATICAL BIOLOGY, 1993, 31 (04) :351-365

← 1 2 3 →