Switching control of two three-dimensional chaotic systems

2015 ◽  
Author(s):  
Sun Changchun ◽  
Xu Qicheng ◽  
Ai Ying
Keyword(s):  
Chaotic Systems ◽  
Three Dimensional ◽  
Switching Control

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

2017 ◽  
Vol 27 (13) ◽  
pp. 1750197 ◽  
Author(s):  
Changchun Sun ◽  
Zhongtang Chen ◽  
Qicheng Xu
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Switching Control ◽  
Mirror Image ◽  
Image System ◽  
Sign Function ◽  
Control Approach ◽  
Switching Law ◽  
Dynamical Behaviors

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

2020 ◽  
Vol 30 (02) ◽  
pp. 2050026 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Special Property ◽  
Computer Search ◽  
Chaotic Flows ◽  
Stable Equilibria ◽  
Dynamical Properties ◽  
Simple Systems ◽  
First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

scholarly journals Synchronization Between Two Different Switched Chaotic Systems By Switching Control

2016 ◽  
Vol 63 ◽  
pp. 01032 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Jie Dong ◽  
Zheng Yu Li
Keyword(s):  
Chaotic Systems ◽  
Switching Control

ROTATING SYNCHRONIZATION IN THREE-DIMENSIONAL CHAOTIC SYSTEMS

2012 ◽  
Vol 26 (20) ◽  
pp. 1250120 ◽  
Author(s):  
FUZHONG NIAN ◽  
XINGYUAN WANG
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Phase Space Reconstruction ◽  
Projective Synchronization ◽  
Reconstruction Method ◽  
Self Similarity ◽  
Application Fields ◽  
Three Dimensional Space

Projective synchronization investigates the synchronization of systems evolve in same orientation, however, in practice, the situation of same orientation is only minority, and the majority is different orientation. This paper investigates the latter, proposes the concept of rotating synchronization, and verifies its necessity and feasibility via theoretical analysis and numerical simulations. Three conclusions were elicited: first, in three-dimensional space, two arbitrary nonlinear chaotic systems who evolve in different orientation can realize synchronization at end; second, projective synchronization is a special case of rotating synchronization, so, the application fields of rotating synchronization is more broadly than that of the former; third, the overall evolving information can be reflected by single state variable's evolving, it has self-similarity, this is the same as the basic idea of phase space reconstruction method, it indicates that we got the same result from different approach, so, our method and the phase space reconstruction method are verified each other.

Generating Chaos from Two Three-Dimensional Rigorous Linear Systems via a Novel Switching Control Approach

2016 ◽  
Vol 26 (13) ◽  
pp. 1650212 ◽  
Author(s):  
Changchun Sun ◽  
Qicheng Xu
Keyword(s):  
Equilibrium Point ◽  
Linear Systems ◽  
Three Dimensional ◽  
Constant Term ◽  
Switching Control ◽  
Numerical Examples ◽  
Absolute Value ◽  
Control Approach ◽  
Switching Law ◽  
Dynamical Behaviors

By constructing two three-dimensional (3D) rigorous linear systems, a novel switching control approach for generating chaos from two linear systems is presented. Two 3D linear systems without any constant term have only one common equilibrium point that is the origin. By employing an absolute-value switching law, chaos can be generated by switching between two linear systems. Basic dynamical behaviors of the systems are investigated in detail. Numerical examples illustrate the effectiveness of the presented approach.

GLOBALLY EXPONENTIALLY ATTRACTIVE SETS AND POSITIVE INVARIANT SETS OF THREE-DIMENSIONAL AUTONOMOUS SYSTEMS WITH ONLY CROSS-PRODUCT NONLINEARITIES

2013 ◽  
Vol 23 (01) ◽  
pp. 1350007 ◽  
Author(s):  
XINQUAN ZHAO ◽  
FENG JIANG ◽  
JUNHAO HU
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Cross Product ◽  
Invariant Set ◽  
Invariant Sets ◽  
Special Cases ◽  
Attractive Sets ◽  
Positive Invariant Set

In this paper, the existence of globally exponentially attractive sets and positive invariant sets of three-dimensional autonomous systems with only cross-product nonlinearities are considered. Sufficient conditions, which guarantee the existence of globally exponentially attractive set and positive invariant set of the system, are obtained. The results of this paper comprise some existing relative results as in special cases. The approach presented in this paper can be applied to study other chaotic systems.

PROJECTIVE SYNCHRONIZATION OF UNIDENTICAL CHAOTIC SYSTEMS BASED ON STABILITY CRITERION

2006 ◽  
Vol 16 (04) ◽  
pp. 1049-1056 ◽  
Author(s):  
HONGJIE YU ◽  
JIANHUA PENG ◽  
YANZHU LIU
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
New Method ◽  
Projective Synchronization ◽  
Partially Linear ◽  
Higher Dimensional ◽  
The Lorenz System ◽  
The Stability

A new method of projective synchronization of unidentical chaotic systems is proposed in this letter. This method is based on the stability criterion of linear systems. The response of two unidentical chaotic systems can synchronize up to any desired scaling factor by a suitable separation of the systems. The new method of projective synchronization is suitable not only for the three-dimensional coupled partially linear systems, but also for higher dimensional even hyperchaotic systems. The simplicity and effectiveness of the proposed method are illustrated by the Lorenz system, the four-dimensional partially linear system, the four-dimensional hyperchaotic Rösser system and Chua's circuit system as four numerical examples.

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