A single three-wing or four-wing chaotic attractor generated from a three-dimensional smooth quadratic autonomous system

2008 ◽  
Vol 38 (4) ◽  
pp. 1187-1196 ◽  
Author(s):  
Zengqiang Chen ◽  
Yong Yang ◽  
Zhuzhi Yuan
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Three Dimensional

A GENERALIZED 3-D FOUR-WING CHAOTIC SYSTEM

2009 ◽  
Vol 19 (11) ◽  
pp. 3841-3853 ◽  
Author(s):  
ZENGHUI WANG ◽  
GUOYUAN QI ◽  
YANXIA SUN ◽  
MICHAËL ANTONIE VAN WYK ◽  
BAREND JACOBUS VAN WYK
Keyword(s):  
Phase Diagrams ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Bifurcation Diagrams ◽  
Basic Properties ◽  
New System

In this paper, several three-dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have similar features. A simpler and generalized 3-D continuous autonomous system is proposed based on these features which can be extended to existing 3-D four-wing chaotic systems by adding some linear and/or quadratic terms. The new system can generate a four-wing chaotic attractor with simple topological structures. Some basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincaré maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

A NEW CHAOTIC ATTRACTOR COINED

2002 ◽  
Vol 12 (03) ◽  
pp. 659-661 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Three Dimensional ◽  
The Other ◽  
Lorenz Attractor ◽  
New Chaotic Attractor

This letter reports the finding of a new chaotic attractor in a simple three-dimensional autonomous system, which connects the Lorenz attractor and Chen's attractor and represents the transition from one to the other.

A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

2009 ◽  
Vol 18 (7) ◽  
pp. 2680-2689 ◽  
Author(s):  
Dong En-Zeng ◽  
Chen Zai-Ping ◽  
Chen Zeng-Qiang ◽  
Yuan Zhu-Zhi
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Three Dimensional

A CHAOTIC SYSTEM WITH ONE SADDLE AND TWO STABLE NODE-FOCI

2008 ◽  
Vol 18 (05) ◽  
pp. 1393-1414 ◽  
Author(s):  
QIGUI YANG ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Autonomous System ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Type Systems ◽  
Stable Node ◽  
Compound Structure ◽  
Chen System

This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations.

YET ANOTHER CHAOTIC ATTRACTOR

1999 ◽  
Vol 09 (07) ◽  
pp. 1465-1466 ◽  
Author(s):  
GUANRONG CHEN ◽  
TETSUSHI UETA
Keyword(s):  
Chaotic Attractor ◽  
Autonomous System ◽  
Three Dimensional

This Letter reports the finding of a new chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.

A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM

2004 ◽  
Vol 14 (05) ◽  
pp. 1507-1537 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Constant Input ◽  
New Class ◽  
Dynamical Behaviors ◽  
Generalized Lorenz System ◽  
New Chaotic System

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-scroll chaotic attractor or confine two attractors to a 2-scroll chaotic attractor under the control of a simple constant input. Furthermore, the concept of generalized Lorenz system is extended to a new class of generalized Lorenz-like systems in a canonical form. Finally, the important problems of classification and normal form of three-dimensional quadratic autonomous chaotic systems are formulated and discussed.

The analysis of complex behaviours of a novel three dimensional autonomous system

2010 ◽  
Vol 19 (7) ◽  
pp. 070514
Author(s):  
Dong Gao-Gao ◽  
Zheng Song ◽  
Tian Li-Xin ◽  
Du Rui-Jin ◽  
Sun Mei
Keyword(s):  
Autonomous System ◽  
Three Dimensional

A 3D Autonomous System with Infinitely Many Chaotic Attractors

2019 ◽  
Vol 29 (12) ◽  
pp. 1950166 ◽  
Author(s):  
Ting Yang ◽  
Qigui Yang
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Autonomous System ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Double Zero ◽  
Finite Dimensional ◽  
Periodic Attractors ◽  
The Stability ◽  
Autonomous Dynamical System

Intuitively, a finite-dimensional autonomous system of ordinary differential equations can only generate finitely many chaotic attractors. Amazingly, however, this paper finds a three-dimensional autonomous dynamical system that can generate infinitely many chaotic attractors. Specifically, this system can generate infinitely many coexisting chaotic attractors and infinitely many coexisting periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many nonhyperbolic double-zero equilibria, and (iii) both infinitely many hyperbolic saddles and nonhyperbolic pure-imaginary equilibria. By analyzing the stability of double-zero and pure-imaginary equilibria, it is shown that the classic Shil’nikov criteria fail in verifying the existence of chaos in the above three cases.

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

Existence of a new three-dimensional chaotic attractor

2009 ◽  
Vol 42 (5) ◽  
pp. 3053-3057 ◽  
Author(s):  
Jiezhi Wang ◽  
Zengqiang Chen ◽  
Zhuzhi Yuan
Keyword(s):  
Chaotic Attractor ◽  
Three Dimensional
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