Stabilizing of Two-Dimensional Discrete Lorenz Chaotic System and Three-Dimensional Discrete Rössler Hyperchaotic System

2009 ◽  
Vol 26 (9) ◽  
pp. 090503 ◽  
Author(s):  
Li Xin ◽  
Chen Yong
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Two Dimensional ◽  
Lorenz Chaotic System

GENERATING HYPERCHAOTIC ATTRACTORS WITH THREE POSITIVE LYAPUNOV EXPONENTS VIA STATE FEEDBACK CONTROL

2009 ◽  
Vol 19 (02) ◽  
pp. 651-660 ◽  
Author(s):  
GUOSI HU
Keyword(s):  
Lyapunov Exponents ◽  
State Feedback ◽  
Electronic Circuit ◽  
Three Dimensional ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
New Hyperchaotic System ◽  
Good Agreement

This letter presents a new hyperchaotic system, which was obtained by adding a nonlinear quadratic controller to the first equation and a linear controller to the second equation of the three-dimensional autonomous modified Lorenz chaotic system. This system uses only two multipliers but can generate very complex strange attractors with three positive Lyapunov exponents. The system is not only demonstrated by numerical simulations but also implemented via an electronic circuit, showing very good agreement with the simulation results.

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

2007 ◽  
Vol 16 (11) ◽  
pp. 3238-3243 ◽  
Author(s):  
Wang Fan-Zhen ◽  
Chen Zeng-Qiang ◽  
Wu Wen-Juan ◽  
Yuan Zhu-Zhi
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Lorenz Chaotic System

Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

2017 ◽  
Vol 27 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Lili Zhou
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Multiple Attractors ◽  
System A ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

scholarly journals Adaptive Modified Function Projective Lag Synchronization of Uncertain Hyperchaotic Dynamical Systems with the Same or Different Dimension and Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xiuli Chai ◽  
Zhihua Gan ◽  
Chunxiao Shi
Keyword(s):  
Dynamical Systems ◽  
Chaotic System ◽  
Control Method ◽  
General Theorem ◽  
Three Dimensional ◽  
Lyapunov Stability Theory ◽  
Hyperchaotic System ◽  
Lag Synchronization ◽  
Projective Lag Synchronization ◽  
Hyperchaotic Systems

Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive control method. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

GENERATING HYPERCHAOTIC ATTRACTORS VIA APPROXIMATE TIME DELAYED STATE FEEDBACK

2008 ◽  
Vol 18 (11) ◽  
pp. 3485-3494 ◽  
Author(s):  
GUOSI HU ◽  
SHIQIN JIANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
State Feedback ◽  
Electronic Circuit ◽  
Hyperchaotic System ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Delayed State Feedback ◽  
New Hyperchaotic System ◽  
Good Agreement

This letter presents a new hyperchaotic system, which was constructed by adding an approximate time delayed state feedback to the second equation of Lorenz chaotic system. The constructed system is not only demonstrated by numerical simulations but also implemented via an electronic circuit, showing very good agreement with the simulation results.

GENERATING HYPERCHAOS VIA STATE FEEDBACK CONTROL

2005 ◽  
Vol 15 (10) ◽  
pp. 3367-3375 ◽  
Author(s):  
YUXIA LI ◽  
WALLACE K. S. TANG ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
State Feedback ◽  
Electronic Circuit ◽  
Three Dimensional ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Nonlinear State

In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.

Design and FPGA implementation of a memristor-based multi-scroll hyperchaotic system

2022 ◽  
Author(s):  
Sheng-Hao Jia ◽  
Yu-Xia Li ◽  
Qing-Yu Shi ◽  
Xia Huang
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Nonlinear Function ◽  
Digital Circuit ◽  
Basins Of Attraction ◽  
Hyperchaotic System ◽  
Digital Implementation ◽  
Dynamical Characteristics ◽  
Novel Method

Abstract In this paper, a novel memristor-based multi-scroll hyperchaotic system is proposed. Based on a voltage-controlled memristor and a modulating sine nonlinear function, a novel method is proposed to generate the multi-scroll hyperchaotic attractors. First, a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function. Then, a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system. Thus, a memristor-based multi-scroll hyperchaotic system is generated, and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures. Moreover, different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters. The Lyapunov exponents, bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system. Besides, the FPGA-based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out. The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope.

The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system

2006 ◽  
Vol 15 (6) ◽  
pp. 1216-1225 ◽  
Author(s):  
Wang Jie-Zhi ◽  
Chen Zeng-Qiang ◽  
Yuan Zhu-Zhi
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Hyperchaotic System

A HYPERCHAOS GENERATED FROM CHEN'S SYSTEM

2006 ◽  
Vol 17 (04) ◽  
pp. 471-478 ◽  
Author(s):  
TIEGANG GAO ◽  
ZENGQIANG CHEN ◽  
ZHUZHI YUAN ◽  
GUANRONG CHEN
Keyword(s):  
Limit Cycle ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Chaos System ◽  
New Hyperchaotic System

This paper presents a new hyperchaotic system, obtained by adding a controller to the second equation of the three-dimensional autonomous Chen's chaotic system. The hyper-chaos system undergoes a change from hyperchaos to limit cycle when the parameter varies. The system is not only demonstrated by computer simulations but also verified with bifurcation analysis.

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Circuit World ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Selcuk Emiroglu ◽  
Akif Akgül ◽  
Yusuf Adıyaman ◽  
Talha Enes Gümüş ◽  
Yılmaz Uyaroglu ◽  
...  
Keyword(s):  
Chaotic System ◽  
Passive Control ◽  
Control Method ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Hyperchaotic System ◽  
Content Type ◽  
Control And Synchronization ◽  
New Hyperchaotic System

Purpose The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented. Design/methodology/approach A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions. Findings The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison. Originality/value The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

Sign in / Sign up

Export Citation Format

Share Document