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.

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.

A HYPERCHAOTIC SYSTEM WITH A FOUR-WING ATTRACTOR

2009 ◽  
Vol 20 (02) ◽  
pp. 323-335 ◽  
Author(s):  
GUOSI HU ◽  
BO YU
Keyword(s):  
System Dynamics ◽  
Lyapunov Exponents ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Topological Structure ◽  
Hyperchaotic System ◽  
Wide Range ◽  
New Chaotic System

Recently, there are many methods for constructing multi-wing/multi-scroll or hyperchaotic attractors; however, it has been noticed that the attractors with both multi-wing topological structure and hyperchaotic characteristic rarely exist. A new chaotic system, obtained by making the change on coordinate to the Hu chaotic system, can generate very complex attractors with four-wing topological structure and three positive Lyapunov exponents over a wide range of parameters. The influence of parameters varying to system dynamics is analyzed, computer simulations and bifurcation analysis is also verified in this paper.

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.

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 New Five Dimensional Hyperchaotic System and its Fractional Order Form

2013 ◽  
Vol 464 ◽  
pp. 375-380 ◽  
Author(s):  
Ling Liu ◽  
Chong Xin Liu ◽  
Yi Fan Liao
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Hyperchaotic System ◽  
Order Form ◽  
Simulation Results ◽  
Predictor Corrector ◽  
New Hyperchaotic System

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

A Novel Hyperchaotic System With Adaptive Control, Synchronization, and Circuit Simulation

2018 ◽  
pp. 382-419 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar ◽  
Aceng Sambas ◽  
Shikha Singh ◽  
Kammogne Soup Tewa Alain ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dissipative System ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
Qualitative Properties ◽  
New Hyperchaotic System

This chapter announces a new four-dimensional hyperchaotic system having two positive Lyapunov exponents, a zero Lyapunov exponent, and a negative Lyapunov exponent. Since the sum of the Lyapunov exponents of the new hyperchaotic system is shown to be negative, it is a dissipative system. The phase portraits of the new hyperchaotic system are displayed with both two-dimensional and three-dimensional phase portraits. Next, the qualitative properties of the new hyperchaotic system are dealt with in detail. It is shown that the new hyperchaotic system has three unstable equilibrium points. Explicitly, it is shown that the equilibrium at the origin is a saddle-point, while the other two equilibrium points are saddle-focus equilibrium points. Thus, it is shown that all three equilibrium points of the new hyperchaotic system are unstable. Numerical simulations with MATLAB have been shown to validate and demonstrate all the new results derived in this chapter. Finally, a circuit design of the new hyperchaotic system is implemented in MultiSim to validate the theoretical model.

CONSTRUCTING MULTIWING HYPERCHAOTIC ATTRACTORS

2010 ◽  
Vol 20 (03) ◽  
pp. 727-734 ◽  
Author(s):  
BO YU ◽  
GUOSI HU
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Topological Structure ◽  
Construction Method ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Simple Construction ◽  
System A ◽  
New Hyperchaotic System ◽  
New System

Few reports have introduced chaotic attractors with both multiwing topological structure and hyperchaotic dynamics. A simple construction method, for designing chaotic system with multiwing attractors, is presented in this paper. The number of wings in the attractor was doubled on applying this method to an arbitrary smooth chaotic system. Moreover, the hyperchaotic property is preserved in the new system. A new hyperchaotic system with 16-wing attractors is constructed; the result system is not only verified via numerical simulation but also confirmed by a DSP-based experiment.

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.

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