Analysis, Control and Circuit Simulation of a Novel 3-D Finance Chaotic System

2016 ◽  
pp. 495-512 ◽  
Author(s):  
S. Vaidyanathan ◽  
Ch. K. Volos ◽  
O. I. Tacha ◽  
I. M. Kyprianidis ◽  
I. N. Stouboulos ◽  
...  
Keyword(s):  
Chaotic System ◽  
Circuit Simulation

scholarly journals Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2145
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng ◽  
Lin Fa
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Time Shift ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
Simulation Results ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.

The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation

2020 ◽  
Vol 30 (15) ◽  
pp. 2050234
Author(s):  
L. Kamdjeu Kengne ◽  
Z. Tabekoueng Njitacke ◽  
J. R. Mboupda Pone ◽  
H. T. Kamdem Tagne
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Nonlinear Behavior ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Unique Contribution ◽  
Chaotic Signals ◽  
Excitation Force

In this paper, the effects of a bias term modeling a constant excitation force on the dynamics of an infinite-equilibrium chaotic system without linear terms are investigated. As a result, it is found that the bias term reduces the number of equilibrium points (transition from infinite-equilibria to only two equilibria) and breaks the symmetry of the model. The nonlinear behavior of the system is highlighted in terms of bifurcation diagrams, maximal Lyapunov exponent plots, phase portraits, and basins of attraction. Some interesting phenomena are found including, for instance, hysteretic dynamics, multistability, and coexisting bifurcation branches when monitoring the system parameters and the bias term. Also, we demonstrate that it is possible to control the offset and amplitude of the chaotic signals generated. Compared to some few cases previously reported on systems without linear terms, the plethora of behaviors found in this work represents a unique contribution in comparison with such type of systems. A suitable analog circuit is designed and used to support the theoretical analysis via a series of Pspice simulations.

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.

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.

Seven Dimension Chaotic System and its Circuit Implementation

2012 ◽  
Vol 588-589 ◽  
pp. 1251-1254 ◽  
Author(s):  
Jian Liang Zhu ◽  
Chun Yu Yu
Keyword(s):  
Chaotic System ◽  
Chaotic Behavior ◽  
Circuit Simulation ◽  
System Simulation ◽  
Chaotic Signal ◽  
Chaotic Attractors ◽  
Signal Source ◽  
Circuit Implementation ◽  
Practical Application ◽  
Signal Encryption

In order to generate more complex chaotic attractors, a seven-dimensional chaotic system is constructed, and relevant chaotic attractors can be obtained by Matlab numerical simulation. Lyapunov exponents validate that the system is chaotic. 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. Chaotic behavior of the system is proved farther. A new chaotic signal source is provided for practical application based on chaos such as secrecy communication and signal encryption fields.

scholarly journals A New Double-Wing Chaotic System With Coexisting Attractors and Line Equilibrium: Bifurcation Analysis and Electronic Circuit Simulation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 115454-115462 ◽  
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Sen Zhang ◽  
Yicheng Zeng ◽  
Mohamad Afendee Mohamed ◽  
...  
Keyword(s):  
Chaotic System ◽  
Bifurcation Analysis ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Coexisting Attractors ◽  
Electronic Circuit Simulation ◽  
Line Equilibrium

Circuit simulation for synchronization of a fractional-order and integer-order chaotic system

2013 ◽  
Vol 73 (3) ◽  
pp. 1671-1686 ◽  
Author(s):  
Diyi Chen ◽  
Cong Wu ◽  
Herbert H. C. Iu ◽  
Xiaoyi Ma
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Circuit Simulation ◽  
Integer Order

scholarly journals Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities

2014 ◽  
Vol 24 (3) ◽  
pp. 375-403 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Viet-Thanh Pham ◽  
Kavitha Madhavan ◽  
Babatunde A. Idowu
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Research Work ◽  
The Novel ◽  
Adaptive Backstepping ◽  
Unknown Parameters ◽  
Circuit Realization ◽  
Backstepping Controller ◽  
Jerk System ◽  
Adaptive Backstepping Controller

Abstract In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model

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