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 Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system

2014 ◽  
Vol 19 (2) ◽  
pp. 272-285 ◽  
Author(s):  
Xiaowen Luo ◽  
Chunhua Wang ◽  
Zhao Wan
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Engineering Application ◽  
Linear Functions ◽  
Chaotic Attractors ◽  
Threshold Limit ◽  
The Lorenz System ◽  
Dissipation Property ◽  
Lyapunov Exponent Spectrum ◽  
New System

Due to the dynamic characteristics of the Lorenz system, multi-wing chaotic systems are still confined in the positive half-space and fail to break the threshold limit. In this paper, a new approach for generating complex grid multi-wing attractors that can break the threshold limit via a novel nonlinear modulating function is proposed from the firstly proposed double-wing chaotic system. The proposed method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. The new system is autonomous and can generate various grid multi-wing butterfly chaotic attractors without requiring any external forcing, it also can produce grid multi-wing both on the xz-plane and yz-plane. Basic properties of the new system such as dissipation property, equilibrium, stability, the Lyapunov exponent spectrum and bifurcation diagram are introduced by numerical simulation, theoretical analysis and circuit experiment, which confirm that the multi-wing attractors chaotic system has more rich and complicated chaotic dynamics. Finally, a novel module-based unified circuit is designed which provides some principles and guidelines for future circuitry design and engineering application. The circuit experimental results are consistent with the numerical simulation results. 

Multiscroll Hyperchaotic System with Hidden Attractors and Its Circuit Implementation

2019 ◽  
Vol 29 (09) ◽  
pp. 1950117 ◽  
Author(s):  
Xin Zhang ◽  
Chunhua Wang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Control Method ◽  
Hyperchaotic System ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
System A ◽  
Simulation Results

Based on the study on Jerk chaotic system, a multiscroll hyperchaotic system with hidden attractors is proposed in this paper, which has infinite number of equilibriums. The chaotic system can generate [Formula: see text] scroll hyperchaotic hidden attractors. The dynamic characteristics of the multiscroll hyperchaotic system with hidden attractors are analyzed by means of dynamic analysis methods such as Lyapunov exponents and bifurcation diagram. In addition, we have studied the synchronization of the system by applying an adaptive control method. The hardware experiment of the proposed multiscroll hyperchaotic system with hidden attractors is carried out using discrete components. The hardware experimental results are consistent with the numerical simulation results of MATLAB and the theoretical analysis results.

scholarly journals A New 4D Chaotic System with Two-Wing, Four-Wing, and Coexisting Attractors and Its Circuit Simulation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Lilian Huang ◽  
Zefeng Zhang ◽  
Jianhong Xiang ◽  
Shiming Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Dynamic Characteristics ◽  
Simulation Analysis ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Coexisting Attractors ◽  
System A ◽  
Simulation Results ◽  
New System

In order to further improve the complexity of chaotic system, a new four-dimensional chaotic system is constructed based on Sprott B chaotic system. By analyzing the system’s phase diagrams, symmetry, equilibrium points, and Lyapunov exponents, it is found that the system can generate not only both two-wing and four-wing attractors but also the attractors with symmetrical coexistence, and the dynamic characteristics of the new system constructed are more abundant. In addition, the system is simulated by Multisim software, and the simulation results show that the results of circuit simulation and numerical simulation analysis are basically the same.

A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

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.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

A Novel Simple Hyperchaotic System with Two Coexisting Attractors

2019 ◽  
Vol 29 (14) ◽  
pp. 1950203 ◽  
Author(s):  
Jiaopeng Yang ◽  
Zhengrong Liu
Keyword(s):  
Complex Dynamics ◽  
Chaotic Dynamic ◽  
Cross Product ◽  
Hyperchaotic System ◽  
Compound Structure ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Periodic Attractors ◽  
New Hyperchaotic System ◽  
New System

This article introduces a new hyperchaotic system of four-dimensional autonomous ordinary differential equations, with only cubic cross-product nonlinearities, which can respectively display two hyperchaotic attractors with only nonhyperbolic equilibria line. Several issues such as basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new hyperchaotic and chaotic system are investigated, either theoretically or numerically. Of particular interest is the fact that the two coexisting attractors of the new hyperchaotic system are symmetrical, and this hyperchaotic system can generate plenty of complex dynamics including two coexisting chaotic or periodic attractors. Moreover, some chaotic features of the attractor are justified numerically. Finally, 0-1 test is used to analyze and describe the complex chaotic dynamic behavior of the new system.

Six-Dimensional Chaotic System and its Circuit Implementation

2011 ◽  
Vol 255-260 ◽  
pp. 2018-2022 ◽  
Author(s):  
Jian Liang Zhu ◽  
Yu Jing Wang ◽  
Shou Qiang Kang
Keyword(s):  
Numerical Simulation ◽  
Power Spectrum ◽  
Chaotic System ◽  
Time Domain ◽  
Circuit Simulation ◽  
System Simulation ◽  
Practical Significance ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Product Term

In order to generate complex chaotic attractors, a six-dimensional chaotic system is designed, which contains six parameters and each equation contains a nonlinear product term. When its parameters satisfy certain conditions, the system is chaotic. By Matlab numerical simulation, chaotic attractor and relevant Lyapunov exponents spectrum can be obtained, which validates that the system is chaotic. And, time domain waveform and power spectrum are shown. Finally, the implementation circuit of this system is designed, and circuit simulation can be done by using Multisim. Circuit simulation result is identical to system simulation completely. The circuit has a practical significance in secrecy communication and correlative fields.

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.

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