THE SCROLL CONTROL AND IMPROVING CASCADE SYNCHRONIZATION OF A NOVEL CHAOTIC SYSTEM

2014 ◽  
Vol 28 (08) ◽  
pp. 1450058 ◽  
Author(s):  
YIN LI ◽  
YULIN ZHAO ◽  
ZHENG-AN YAO
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Numerical Results ◽  
Cascade Method ◽  
New System

In this paper, on the basis of the Laypunov stability and the cascade synchronization approach, an effectual scroll controller and improving cascade synchronization approach are derived. The chaotic attractor can be displayed to be lopsided, till to be 1-scroll and periodic via the different scroll controller. And the proposed synchronization technique is applied to the new system, which the synchronization controller obtained by improving cascade method and adaptive functions. Numerical results are used to verify the effectiveness of the scheme.

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 Around a Pre-Located Ring

2017 ◽  
Vol 27 (10) ◽  
pp. 1750152 ◽  
Author(s):  
Zhen Wang ◽  
Zhe Xu ◽  
Ezzedine Mliki ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Chaotic Systems ◽  
Specific Property ◽  
Unique Property ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
New Chaotic Attractor ◽  
New System

Designing chaotic systems with specific features is a very interesting topic in nonlinear dynamics. However most of the efforts in this area are about features in the structure of the equations, while there is less attention to features in the topology of strange attractors. In this paper, we introduce a new chaotic system with unique property. It has been designed in such a way that a specific property has been injected to it. This new system is analyzed carefully and its real circuit implementation is presented.

scholarly journals A New Four-Scroll Chaotic Attractor Consisted of Two-Scroll Transient Chaotic and Two-Scroll Ultimate Chaotic

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yuhua Xu ◽  
Bing Li ◽  
Yuling Wang ◽  
Wuneng Zhou ◽  
Jian-an Fang
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
The Other ◽  
Phase Portraits ◽  
Fractional Dimension ◽  
The Novel ◽  
New Chaotic System ◽  
New System

A new four-scroll chaotic attractor is found by feedback controlling method in this paper. The novel chaotic system can generate four scrolls two of which are transient chaotic and the other two of which are ultimate chaotic. Of particular interest is that this novel chaotic system can generate one-scroll, two 2-scroll and four-scroll chaotic attractor with variation of a single parameter. We analyze the new system by means of phase portraits, Lyapunov exponents, fractional dimension, bifurcation diagram, and Poincaré map, respectively. The analysis results show clearly that this is a new chaotic system which deserves further detailed investigation.

A New Grid Multi-Scroll Chaotic System and the Simulation Based on Labview

2012 ◽  
Vol 538-541 ◽  
pp. 2666-2669
Author(s):  
Yong Huang
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Step Function ◽  
Simulation System ◽  
Unstable System ◽  
Simulation Based ◽  
Two Parameters ◽  
The Way

In order to get the grid Multi-Scroll in the two directions, based on a simple unstable system, the way of the combination of the translational transform and step function was put forward to make the scrolls extending in the x and y directions in this paper. The quantity of scrolls can be controlled by two parameters N and M. A simulation system was designed with Labview to simulate grid Multi-Scroll chaotic system, it demonstrates the existence of grid Multi-Scroll chaotic attractor.

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

SHIL'NIKOV HETEROCLINIC ORBITS IN A CHAOTIC SYSTEM

2007 ◽  
Vol 21 (25) ◽  
pp. 4429-4436 ◽  
Author(s):  
FENG-YUN SUN
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Heteroclinic Orbits ◽  
Geometric Structures ◽  
Undetermined Coefficient ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

In this paper, a chaotic system which exhibits a chaotic attractor with only three equilibria for some parameters is considered. The existence of heteroclinic orbits of the Shil'nikov type in a chaotic system has been proved using the undetermined coefficient method. As a result, the Shil'nikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of the attractor are determined by these heteroclinic orbits.

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.

scholarly journals A Novel 2D – Grid of Scroll Chaotic Attractor Generated by CNN

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 99 ◽  
Author(s):  
Ahmed M. Ali ◽  
Saif M. Ramadhan ◽  
Fadhil R. Tahir
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Attractor ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Electronic Circuits ◽  
Nonlinear Networks ◽  
Design And Implementation ◽  
Simulation Results ◽  
New System

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x=y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (1×3) cells. The paper concerns on the design and implementation of 2×2 and 3×3 2D-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

Memristor Oscillators and its FPGA Implementation

2011 ◽  
Vol 383-390 ◽  
pp. 6992-6997 ◽  
Author(s):  
Ai Xue Qi ◽  
Cheng Liang Zhang ◽  
Guang Yi Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Chaotic Attractor ◽  
Hardware Implementation ◽  
Fpga Implementation ◽  
Experimental Results ◽  
Linear Resistance ◽  
Non Linear ◽  
Field Programmable

This paper presents a method that utilizes a memristor to replace the non-linear resistance of typical Chua’s circuit for constructing a chaotic system. The improved circuit is numerically simulated in the MATLAB condition, and its hardware implementation is designed using field programmable gate array (FPGA). Comparing the experimental results with the numerical simulation, the two are the very same, and be able to generate chaotic attractor.

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