Analysis and Circuit Simulation of New Five Terms Chaotic System

2013 ◽  
Vol 275-277 ◽  
pp. 825-829 ◽  
Author(s):  
Guo Qing Huang
Keyword(s):  
Numerical Simulation ◽  
Power Spectrum ◽  
Differential Equations ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Theory Analysis ◽  
New Chaotic Attractor

A new chaotic attractor is reported with only five terms in three simple differential equations. The system is not only studied via theory analysis and numerical simulation, such as Lyapunov exponents, power spectrum and poincaré section and bifurcations diagrams, but also implemented via an electronic circuit designed by Multisim software

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.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

2017 ◽  
Vol 27 (09) ◽  
pp. 1750142 ◽  
Author(s):  
Qiang Lai ◽  
Akif Akgul ◽  
Xiao-Wen Zhao ◽  
Huiqin Pei
Keyword(s):  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Limit Cycles ◽  
Electronic Circuit ◽  
Strange Attractors ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors ◽  
Signum Function ◽  
Multiple Coexisting Attractors

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

A New Dynamic System Analysis

2013 ◽  
Vol 392 ◽  
pp. 222-226
Author(s):  
Bao Liang Mi ◽  
Guo Zeng Wu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic System ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
System Analysis ◽  
Electronic Circuit ◽  
Circuit Implementation ◽  
Dynamical Properties ◽  
Electronic Circuit Implementation

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

Memristor Oscillators and its FPGA Implementation

2011 ◽  
Vol 383-390 ◽  
pp. 6992-6997 ◽  
Author(s):  
Ai Xue Qi ◽  
Cheng Liang Zhang ◽  
Guang Yi Wang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Chaotic Attractor ◽  
Hardware Implementation ◽  
Fpga Implementation ◽  
Experimental Results ◽  
Linear Resistance ◽  
Non Linear ◽  
Field Programmable

This paper presents a method that utilizes a memristor to replace the non-linear resistance of typical Chua’s circuit for constructing a chaotic system. The improved circuit is numerically simulated in the MATLAB condition, and its hardware implementation is designed using field programmable gate array (FPGA). Comparing the experimental results with the numerical simulation, the two are the very same, and be able to generate chaotic attractor.

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.

GENERATION OF AN EIGHT-WING CHAOTIC ATTRACTOR FROM QI 3-D FOUR-WING CHAOTIC SYSTEM

2012 ◽  
Vol 22 (12) ◽  
pp. 1250287 ◽  
Author(s):  
GUOYUAN QI ◽  
ZHONGLIN WANG ◽  
YANLING GUO
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Poincaré Map ◽  
Electronic Circuit ◽  
Constant Parameter ◽  
Poincare Map ◽  
Compound Structure ◽  
Topological Structures ◽  
Dynamical Behaviors ◽  
Map Analysis

This paper presents an eight-wing chaotic attractor by replacing a constant parameter with a switch function in Qi four-wing 3-D chaotic system. The eight-wing chaotic attractor has more complicated topological structures and dynamics than the original one. Some basic dynamical behaviors and the compound structure of the proposed 3-D system are investigated. Poincaré-map analysis shows that the system has an extremely rich dynamics. The physical existence of the eight-wing chaotic attractor is verified by an electronic circuit FPGA.

scholarly journals Analysis of a New Quadratic 3D Chaotic Attractor

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shahed Vahedi ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Bifurcation Diagrams ◽  
Basic Properties ◽  
Undetermined Coefficient ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

A new three-dimensional chaotic system is introduced. Basic properties of this system show that its corresponding attractor is topologically different from some well-known systems. Next, detailed information on dynamic of this system is obtained numerically by means of Lyapunov exponents spectrum, bifurcation diagrams, and 0-1 chaos indicator test. We finally prove existence of this chaotic attractor theoretically using Shil’nikov theorem and undetermined coefficient method.

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

A GENERALIZED 3-D FOUR-WING CHAOTIC SYSTEM

2009 ◽  
Vol 19 (11) ◽  
pp. 3841-3853 ◽  
Author(s):  
ZENGHUI WANG ◽  
GUOYUAN QI ◽  
YANXIA SUN ◽  
MICHAËL ANTONIE VAN WYK ◽  
BAREND JACOBUS VAN WYK
Keyword(s):  
Phase Diagrams ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Bifurcation Diagrams ◽  
Basic Properties ◽  
New System

In this paper, several three-dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have similar features. A simpler and generalized 3-D continuous autonomous system is proposed based on these features which can be extended to existing 3-D four-wing chaotic systems by adding some linear and/or quadratic terms. The new system can generate a four-wing chaotic attractor with simple topological structures. Some basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincaré maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

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