A New 3D Chaotic System with only Quadratic Nonlinearities: Analysis and Circuit Implantation

2021 ◽  
pp. 587-594
Author(s):  
Seyede Sanaz Hosseini ◽  
Mohammad-Ali Jafari ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Quadratic Nonlinearities

scholarly journals Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1= 0.0395,L2= 0 and L3= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

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>

scholarly journals A New 4-D Chaotic System with Hidden Attractor and its Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1245 ◽  
Author(s):  
Aceng Sambas ◽  
Mustafa Mamat ◽  
Sundarapandian Vaidyanathan ◽  
Muhammad Mohamed ◽  
Mada Sanjaya
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Hidden Attractor ◽  
Circuit Realization ◽  
New Chaotic System ◽  
Quadratic Nonlinearities ◽  
Work First

In the chaos literature, there is currently significant interest in the discovery of new chaotic systems with hidden chaotic attractors. A new 4-D chaotic system with only two quadratic nonlinearities is investigated in this work. First, we derive a no-equilibrium chaotic system and show that the new chaotic system exhibits hidden attractor. Properties of the new chaotic system are analyzed by means of phase portraits, Lyapunov chaos exponents, and Kaplan-Yorke dimension. Then an electronic circuit realization is shown to validate the chaotic behavior of the new 4-D chaotic system. Finally, the physical circuit experimental results of the 4-D chaotic system show agreement with numerical simulations.

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 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control

2016 ◽  
Vol 26 (1) ◽  
pp. 19-47 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Method ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Recursive Procedure ◽  
Quadratic Nonlinearities

This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1= 0.20572,L2= 0 and L3= −1.20824. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the novel jerk chaotic system is derived as DKY= 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.

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