A New Chaotic Attractor and its Digital Implementation Based on LabVIEW

2013 ◽  
Vol 278-280 ◽  
pp. 54-57
Author(s):  
Hong Yang
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Theoretical Simulation ◽  
Digital Implementation ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
External Conditions ◽  
New Chaotic Attractor ◽  
Implementation Method

In this paper, a novel three-dimensional autonomous chaotic system with six terms and two quadratic nonlinearities is presented. Some basic dynamical properties of the new chaotic system are analyzed by means of equilibrium points, eigenvalue structures, Lyapunov exponent and Lyapunov dimension. In order to overcome the external conditions affected by the analog circuit’s chaotic system, digital implementation of the new chaotic system based on LabVIEW is also proposed. The results show that the experimental results by LabVIEW are consistent with the theoretical simulation results by Matlab, and the method is an effective digital implementation method.

scholarly journals A Novel Chaotic System with Two Circles of Equilibrium Points: Multistability, Electronic Circuit and FPGA Realization

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1211 ◽  
Author(s):  
Sambas ◽  
Vaidyanathan ◽  
Tlelo-Cuautle ◽  
Zhang ◽  
Sukono ◽  
...  
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Digital Implementation ◽  
Gate Arrays ◽  
New Chaotic System ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Good Agreement

This paper introduces a new chaotic system with two circles of equilibrium points. The dynamical properties of the proposed dynamical system are investigated through evaluating Lyapunov exponents, bifurcation diagram and multistability. The qualitative study shows that the new system exhibits coexisting periodic and chaotic attractors for different values of parameters. The new chaotic system is implemented in both analog and digital electronics. In the former case, we introduce the analog circuit of the proposed chaotic system with two circles of equilibrium points using amplifiers, which is simulated in MultiSIM software, version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB. In addition, we perform the digital implementation of the new chaotic system using field-programmable gate arrays (FPGA), the experimental observations of the attractors of which confirm its suitability to generate chaotic behavior.

A NEW CHAOTIC SYSTEM AND ITS GENERATION

2003 ◽  
Vol 13 (01) ◽  
pp. 261-267 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamical Behaviors ◽  
New Chaotic System

This Letter introduces a relatively simple three-dimensional continuous autonomous chaotic system, which can display complex 2- and 4-scroll attractors in simulations. Its generation and basic dynamical behaviors are briefly described.

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.

Jacobi analysis for an unusual 3D autonomous system

2020 ◽  
Vol 17 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Chunsheng Feng ◽  
Qiujian Huang ◽  
Yongjian Liu
Keyword(s):  
Chaotic System ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Chen System ◽  
Parameter Region ◽  
Stable Equilibria ◽  
The Lorenz System ◽  
Deviation Vector

Little seems to be known about the study of the chaotic system with only Lyapunov stable equilibria from the perspective of differential geometry. Therefore, this paper presents Jacobi analysis of an unusual three-dimensional (3D) autonomous chaotic system. Under certain parameter conditions, this system has positive Lyapunov exponents and only two linear stable equilibrium points, which means that chaotic attractor and Lyapunov stable equilibria coexist. The dynamical behavior of the deviation vector near the whole trajectories (including all equilibrium points) is analyzed in detail. The results show that the value of the deviation curvature tensor at equilibrium points is only related to parameters; the two equilibrium points of the system are Jacobi stable if the parameters satisfy certain conditions. Particularly, for a specific set of parameters, the linear stable equilibrium points of the system are always Jacobi unstable. A periodic orbit that is Lyapunov stable is also proven to be always Jacobi unstable. Next, Jacobi-stable regions of the Lorenz system, the Chen system and the system under study are compared for specific parameters. It can be found that although these three chaotic systems are very similar, their regions of Jacobi stable parameters are much different. Finally, by comparing Jacobi stability with Lyapunov stability, the obtained results demonstrate that the Jacobi stable parameter region is basically symmetric with the Lyapunov stable parameter region.

scholarly journals A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

scholarly journals Image Encryption Scheme with Compressed Sensing Based on New Three-Dimensional Chaotic System

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 819 ◽  
Author(s):  
Yaqin Xie ◽  
Jiayin Yu ◽  
Shiyu Guo ◽  
Qun Ding ◽  
Erfu Wang
Keyword(s):  
Compressed Sensing ◽  
Image Encryption ◽  
Chaotic System ◽  
Three Dimensional ◽  
Encryption Algorithm ◽  
Encryption Scheme ◽  
High Complexity ◽  
Measurement Matrix ◽  
The Core ◽  
New Chaotic System

In this paper, a new three-dimensional chaotic system is proposed for image encryption. The core of the encryption algorithm is the combination of chaotic system and compressed sensing, which can complete image encryption and compression at the same time. The Lyapunov exponent, bifurcation diagram and complexity of the new three-dimensional chaotic system are analyzed. The performance analysis shows that the chaotic system has two positive Lyapunov exponents and high complexity. In the encryption scheme, a new chaotic system is used as the measurement matrix for compressed sensing, and Arnold is used to scrambling the image further. The proposed method has better reconfiguration ability in the compressible range of the algorithm compared with other methods. The experimental results show that the proposed encryption scheme has good encryption effect and image compression capability.

AN UNUSUAL 3D AUTONOMOUS QUADRATIC CHAOTIC SYSTEM WITH TWO STABLE NODE-FOCI

2010 ◽  
Vol 20 (04) ◽  
pp. 1061-1083 ◽  
Author(s):  
QIGUI YANG ◽  
ZHOUCHAO WEI ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Type Systems ◽  
Homoclinic Orbits ◽  
Stable Node ◽  
Algebraic Form ◽  
Special Cases ◽  
New Chaotic System ◽  
Parameter Values ◽  
New System

This paper reports the finding of an unusual three-dimensional autonomous quadratic Lorenz-like chaotic system which, surprisingly, has two stable node-type of foci as its only equilibria. The new system contains the diffusionless Lorenz system and the Burke–Shaw system, and some others, as special cases. The algebraic form of the new chaotic system is similar to the other Lorenz-type systems, but they are topologically nonequivalent. To further analyze the new system, some dynamical behaviors such as Hopf bifurcation and singularly degenerate heteroclinic and homoclinic orbits, are rigorously proved with simulation verification. Moreover, it is proved that the new system with some specified parameter values has Silnikov-type homoclinic and heteroclinic chaos.

scholarly journals A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design

2019 ◽  
Vol 9 (4) ◽  
pp. 2336 ◽  
Author(s):  
Aceng Sambas ◽  
Mustafa Mamat ◽  
Ayman Ali Arafa ◽  
Gamal M Mahmoud ◽  
Mohamad Afendee Mohamed ◽  
...  
Keyword(s):  
Circuit Design ◽  
Chaotic System ◽  
Passive Control ◽  
Electronic Circuit ◽  
Control Method ◽  
Phase Portraits ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
Line Of Equilibria ◽  
Line Equilibrium

<p>A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the  new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study.</p>

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