scholarly journals A New Chaotic System with Stable Equilibrium: Entropy Analysis, Parameter Estimation, and Circuit Design

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 670 ◽  
Author(s):  
Tomasz Kapitaniak ◽  
S. Mohammadi ◽  
Saad Mekhilef ◽  
Fawaz Alsaadi ◽  
Tasawar Hayat ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Circuit Design ◽  
Chaotic System ◽  
Stable Equilibrium ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Equilibrium Analysis ◽  
Entropy Analysis ◽  
New Chaotic System ◽  
Multistable Systems

In this paper, we introduce a new, three-dimensional chaotic system with one stable equilibrium. This system is a multistable dynamic system in which the strange attractor is hidden. We investigate its dynamic properties through equilibrium analysis, a bifurcation diagram and Lyapunov exponents. Such multistable systems are important in engineering. We perform an entropy analysis, parameter estimation and circuit design using this new system to show its feasibility and ability to be used in engineering applications.

A New 3D Cubic Chaotic System and its Circuitry Implementation

2011 ◽  
Vol 130-134 ◽  
pp. 3924-3927
Author(s):  
Wei Deng ◽  
Yan Feng Wang ◽  
Jie Fang
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Electronic Circuit ◽  
Nonlinear Term ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Lyapunov Dimension ◽  
New Chaotic System ◽  
Lyapunov Exponent Spectrum ◽  
New System

A new three-dimensional cubic chaotic system is reported. This new system contains five system parameters and each equation contains nonlinear term. Moreover, two equations of nonlinear term is cubic. The basic properties of the new system are investigated via theoretical analysis, numerical simulation, Lyapunov exponent spectrum, bifurcation diagram, Lyapunov dimension and Poincare diagram. The different dynamic behaviors of the new system are analyzed when each system parameter is changed .An electronic circuit was designed to realize the new chaotic system. Experimental chaotic behaviors of the system were found to be identical to the dynamic properties predicted by theoretical analysis and numerical simulations.

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 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.

A new three-dimensional chaotic system: its adaptive control and circuit design

2019 ◽  
Vol 13 (1) ◽  
pp. 101
Author(s):  
Gambo Betchewe ◽  
Mohamadou Alidou ◽  
Sundarapandian Vaidyanathan ◽  
Oumate Alhadji Abba
Keyword(s):  
Adaptive Control ◽  
Circuit Design ◽  
Chaotic System ◽  
Three Dimensional

scholarly journals A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation

Entropy ◽  
2018 ◽  
Vol 20 (2) ◽  
pp. 86 ◽  
Author(s):  
Guanghui Xu ◽  
Yasser Shekofteh ◽  
Akif Akgül ◽  
Chunbiao Li ◽  
Shirin Panahi
Keyword(s):  
Parameter Estimation ◽  
Chaotic System ◽  
New Chaotic System ◽  
Measurement Signal ◽  
Entropy Measurement ◽  
Signal Encryption

Circuit Design Contains a Class of Squared Term Lorenz Family Chaotic System

2014 ◽  
Vol 602-605 ◽  
pp. 2684-2687
Author(s):  
Yu Zhang ◽  
Chong Lou Tong ◽  
Teng Fei Lei
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Circuit Design ◽  
Chaotic System ◽  
Lorenz System ◽  
Three Dimensional ◽  
System Stability ◽  
Experimental Simulation ◽  
Chaotic Circuit ◽  
New Class

A new class of three-dimensional chaotic system is constructed by algebraic methods, which has a similar structure with the classic Lorenz system but contains the square term. The equilibrium point of the system stability is analyzed, and the numerical simulation is carried on the bifurcation diagram and Lyapunov exponent. The chaotic circuit of these systems is designed by using the software of EWB. The results of the experimental simulation verify the existence of the chaotic attractor, which provides theoretical reference to the application of such system.

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