scholarly journals Design and application of multi-scroll chaotic attractors based on simplified Lorenz system

2014 ◽  
Vol 63 (12) ◽  
pp. 120511
Author(s):  
Ai Xing-Xing ◽  
Sun Ke-Hui ◽  
He Shao-Bo ◽  
Wang Hui-Hai
Keyword(s):  
Lorenz System ◽  
Chaotic Attractors ◽  
Simplified Lorenz System ◽  
Design And Application

CHAOTIC ATTRACTORS OF THE CONJUGATE LORENZ-TYPE SYSTEM

2007 ◽  
Vol 17 (11) ◽  
pp. 3929-3949 ◽  
Author(s):  
QIGUI YANG ◽  
GUANRONG CHEN ◽  
KUIFEI HUANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Type System ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Chen System ◽  
Numerical Examples ◽  
Special Cases ◽  
Dynamical Properties

A new conjugate Lorenz-type system is introduced in this paper. The system contains as special cases the conjugate Lorenz system, conjugate Chen system and conjugate Lü system. Chaotic dynamics of the system in the parametric space is numerically and thoroughly investigated. Meanwhile, a set of conditions for possible existence of chaos are derived, which provide some useful guidelines for searching chaos in numerical simulations. Furthermore, some basic dynamical 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 demonstrated with various numerical examples.

BIFURCATIONS AND CHAOS IN FRACTIONAL-ORDER SIMPLIFIED LORENZ SYSTEM

2010 ◽  
Vol 20 (04) ◽  
pp. 1209-1219 ◽  
Author(s):  
KEHUI SUN ◽  
XIA WANG ◽  
J. C. SPROTT
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Fractional Order Systems ◽  
Wide Range ◽  
The Time Domain ◽  
Fractional Orders ◽  
Simplified Lorenz System

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

scholarly journals A New Fractional-Order Chaotic Complex System and Its Antisynchronization

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Cuimei Jiang ◽  
Shutang Liu ◽  
Chao Luo
Keyword(s):  
Complex System ◽  
Fractional Order ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Fractional Order Systems ◽  
Chaotic Complex System ◽  
The Stability ◽  
Complex Lorenz System

We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme.

Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method

2012 ◽  
Vol 542-543 ◽  
pp. 1042-1046 ◽  
Author(s):  
Xin Deng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
The Lorenz System ◽  
Lu System

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system

2012 ◽  
Vol 69 (3) ◽  
pp. 1383-1391 ◽  
Author(s):  
Keihui Sun ◽  
Xuan Liu ◽  
Congxu Zhu ◽  
J. C. Sprott
Keyword(s):  
Lorenz System ◽  
Hyperchaos Control ◽  
Simplified Lorenz System

A UNIFIED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2006 ◽  
Vol 16 (10) ◽  
pp. 2855-2871 ◽  
Author(s):  
QIGUI YANG ◽  
GUANGRONG CHEN ◽  
TIANSHOU ZHOU
Keyword(s):  
Canonical Form ◽  
Special Form ◽  
Lorenz System ◽  
Type System ◽  
Chaotic Attractors ◽  
Lorenz Attractor ◽  
System A ◽  
Generalized Lorenz System ◽  
Two Parameters ◽  
First Time

Based on the generalized Lorenz system, a conjugate Lorenz-type system is introduced, and a new unified Lorenz-type system containing these two classes of systems is naturally constructed in the paper. Such a unified system is state-equivalent to a simple special form, which is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, three new chaotic attractors, called conjugate attractors, are found for the first time, which are conjugate to the Lorenz attractor, the Chen attractor, and the Lü attractor, respectively.

Characteristic Analysis and DSP Realization of Fractional-Order Simplified Lorenz System Based on Adomian Decomposition Method

2015 ◽  
Vol 25 (06) ◽  
pp. 1550085 ◽  
Author(s):  
Huihai Wang ◽  
Kehui Sun ◽  
Shaobo He
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Lorenz System ◽  
Adomian Decomposition Method ◽  
Qr Factorization ◽  
Iteration Step ◽  
Phase Portraits ◽  
Characteristic Analysis ◽  
Adomian Decomposition ◽  
Simplified Lorenz System

By adopting Adomian decomposition method, the fractional-order simplified Lorenz system is solved and implemented on a digital signal processor (DSP). The Lyapunov exponent (LE) spectra of the system is calculated based on QR-factorization, and it accords well with the corresponding bifurcation diagrams. We analyze the influence of the parameter and the fractional derivative order on the system characteristics by color maximum LE (LEmax) and chaos diagrams. It is found that the smaller the order is, the larger the LEmax is. The iteration step size also affects the lowest order at which the chaos exists. Further, we implement the fractional-order simplified Lorenz system on a DSP platform. The phase portraits generated on DSP are consistent with the results that were obtained by computer simulations. It lays a good foundation for applications of the fractional-order chaotic systems.

DESIGN AND IMPLEMENTATION OF MULTI-WING BUTTERFLY CHAOTIC ATTRACTORS VIA LORENZ-TYPE SYSTEMS

2010 ◽  
Vol 20 (01) ◽  
pp. 29-41 ◽  
Author(s):  
SIMIN YU ◽  
WALLACE K. S. TANG ◽  
JINHU LÜ ◽  
GUANRONG CHEN
Keyword(s):  
Analog Circuits ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Type Systems ◽  
Circuit Diagram ◽  
Chaotic Attractors ◽  
Dynamical Behaviors ◽  
Novel Approach ◽  
Index 2 ◽  
First Time

Lorenz system, as the first classical chaotic system, has been intensively investigated over the last four decades. Based on the sawtooth wave function, this paper initiates a novel approach for generating multi-wing butterfly chaotic attractors from the generalized first and second kinds of Lorenz-type systems. Compared with the traditional ring-shaped multi-scroll Lorenz chaotic attractors, the proposed multi-wing butterfly chaotic attractors are much easier to be designed and implemented by analog circuits. The dynamical behaviors of these multi-wing butterfly chaotic systems are further studied. Theoretical analysis shows that every index-2 saddle-focus equilibrium corresponds to a unique wing in the butterfly attractors. Finally, a module-based unified circuit diagram is constructed for realizing various multi-wing butterfly attractors. It should be especially pointed out that this is the first time in the literature that a maximal 10-wing butterfly chaotic attractor is experimentally verified by analog circuits.

Modeling and analysis of dynamics for a 3D mixed Lorenz system with a damped term

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xianyi Li ◽  
Umirzakov Mirjalol
Keyword(s):  
Vector Fields ◽  
Lorenz System ◽  
Global Analysis ◽  
Three Dimensional ◽  
Heteroclinic Orbits ◽  
Chaotic Attractors ◽  
Polynomial Vector Fields ◽  
Poincaré Compactification ◽  
Modeling And Analysis ◽  
Analysis Of Dynamics

Abstract The work in this paper consists of two parts. The one is modelling. After a method of classification for three dimensional (3D) autonomous chaotic systems and a concept of mixed Lorenz system are introduced, a mixed Lorenz system with a damped term is presented. The other is the analysis for dynamical properties of this model. First, its local stability and bifurcation in its parameter space are in detail considered. Then, the existence of its homoclinic and heteroclinic orbits, and the existence of singularly degenerate heteroclinic cycles, are studied by rigorous theoretical analysis. Finally, by using the Poincaré compactification for polynomial vector fields in R 3 ${\mathbb{R}}^{3}$ , a global analysis of this system near and at infinity is presented, including the complete description of its dynamics on the sphere near and at infinity. Simulations corroborate corresponding theoretical results. In particular, a possibly new mechanism for the creation of chaotic attractors is proposed. Some different structure types of chaotic attractors are correspondingly and numerically found.

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