A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

A fifth-order multiple-scale solution for Hopf bifurcations

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2723-2731 ◽  
Author(s):  
D. Dessi ◽  
F. Mastroddi ◽  
L. Morino
Keyword(s):  
Multiple Scale ◽  
Hopf Bifurcations ◽  
Fifth Order

Hopf bifurcations in Langmuir circulations

1992 ◽  
Vol 59 (1-3) ◽  
pp. 226-254 ◽  
Author(s):  
Stephen M. Cox ◽  
Sidney Leibovich ◽  
Irene M. Moroz ◽  
Amit Tandon
Keyword(s):  
Hopf Bifurcations ◽  
Langmuir Circulations
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