Generation and Circuit Implementation of Grid Multi-Scroll Chaotic Attractors

2013 ◽  
Vol 336-338 ◽  
pp. 1554-1557
Author(s):  
Chao Xia Zhang
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Maximum Lyapunov Exponent ◽  
Circuit Implementation

In this paper, grid multi-scroll chaotic attractors are firstly generated. The maximum Lyapunov exponent is further calculated to prove the existence of chaos in designed system. An improved module-based circuit is designed for realizing 5×3 grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.

A Novel Four-Order Chaotic System with N-Attractor Multi-Direction Multi-Scroll Attractors

2014 ◽  
Vol 678 ◽  
pp. 81-88
Author(s):  
Wen Shuang Yin ◽  
Dai Jun Wei ◽  
Shi Qiang Chen
Keyword(s):  
Lyapunov Exponent ◽  
Bifurcation Diagram ◽  
Chaotic System ◽  
Operational Amplifier ◽  
Experimental Results ◽  
Order System ◽  
Chaotic Attractors ◽  
Maximum Lyapunov Exponent ◽  
Nonlinear Functions ◽  
New System

In this paper, a novel four-order system is proposed. It can generate N-attractor multi-direction multi-scroll attractor by adding simple nonlinear functions. We analyze the new system by using means of maximum Lyapunov exponent, bifurcation diagram and Poincaré maps of the system. Moreover, an minimum operational amplifier circuit is designed for realizing 2×(3×3 ×3) scroll chaotic attractors, and experimental results are also obtained, which verify chaos characteristics of the system.

Multi-Scroll Chaotic System Based on Even-Symmetric Step-Wave Sequence Control

2013 ◽  
Vol 340 ◽  
pp. 760-766 ◽  
Author(s):  
Zi Long Tang ◽  
Si Min Yu
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Switching Control ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
New Approach ◽  
Piecewise Linearity ◽  
Index 2

This paper presents a new approach for generating multi-scroll chaotic attractors. First, a new double scroll chaotic system with piecewise linearity and invariance under the transformationis introduced. Then, by using the even-symmetric step-wave sequence switching control method in this system to extend the number of saddle-focus points of index 2, the intended multi-scroll chaotic attractors can be obtained. A circuit for generating multi-scroll chaotic attractors is designed, and the experimental results are also given, confirming the consistency of the theory design and circuit implementation.

scholarly journals Chaotic Saddles in a Generalized Lorenz Model of Magnetoconvection

2020 ◽  
Vol 30 (12) ◽  
pp. 2030034
Author(s):  
Francis F. Franco ◽  
Erico L. Rempel
Keyword(s):  
Nonlinear Dynamics ◽  
Fractal Dimension ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Chaotic Attractors ◽  
Maximum Lyapunov Exponent ◽  
Lorenz Model ◽  
Fractal Basin Boundaries ◽  
Chaotic Transients ◽  
Basin Boundaries

The nonlinear dynamics of a recently derived generalized Lorenz model [ Macek & Strumik, 2010 ] of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where attractors and nonattracting chaotic sets coexist inside a periodic window. The nonattracting chaotic sets, also called chaotic saddles, are responsible for fractal basin boundaries with a fractal dimension near the dimension of the phase space, which causes the presence of very long chaotic transients. It is shown that the chaotic saddles can be used to infer properties of chaotic attractors outside the periodic window, such as their maximum Lyapunov exponent.

Generation and Circuit Implementation of Multi-Scroll Chaotic Attractors with Controllable Direction

2014 ◽  
Vol 513-517 ◽  
pp. 4559-4562
Author(s):  
Xiao Wen Luo ◽  
Chun Hua Wang
Keyword(s):  
Lyapunov Exponent ◽  
Control Function ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Relative Coefficient ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

An approach for generating multi-scroll chaotic attractors with controllable direction in one plane is proposed. Firstly, an appropriate nonlinear function is selected to control the number and direction of multi-scroll chaotic attractors in the three-order Jerk system. Then, we add new control function to Jerk system and observe Lyapunov exponent spectrum of relative coefficient and the change of equilibrium points. Different multi-scroll chaotic attractors with controllable direction are generated by adjusting the coefficient of the control function in a plane. The implementation of circuit verifies the feasibility of this method.

ON LORENZ-LIKE DYNAMIC SYSTEMS WITH STRENGTHENED NONLINEARITY AND NEW PARAMETERS

2010 ◽  
Vol 08 (02) ◽  
pp. 293-311 ◽  
Author(s):  
BO LIAO ◽  
YUAN YAN TANG ◽  
LU AN
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Dynamic Systems ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Maximum Lyapunov Exponent ◽  
Preliminary Results ◽  
Quadratic Equations

This paper introduces two types of Lorenz-like three-dimensional quadratic autonomous chaotic systems with 7 and 8 new parameters free of choice, respectively. Both systems are investigated at the equilibriums to study their chaotic characteristics. We focus our attention on the second type of the introduced system which consists of three nonlinear quadratic equations. Predictably, coordinates of the equilibriums are prohibitively complex. Therefore, instead of directly analyzing their stability, we prove the asymptotical characterization of equilibriums by utilizing our preliminary results derived for the first type of system. Our result shows that, though the coordinates of equilibriums satisfy a ternary quadratic, the system still contains only three equilibriums in circumstances of chaos. Sufficient conditions for the chaotic appearance of systems are derived. Our results are further verified by numerical simulations and the maximum Lyapunov exponent for several examples. Our research takes a first step in investigating chaos in Lorenz-like dynamic systems with strengthened nonlinearity and general forms of parameters.

Design of Grid Multiscroll Chaotic Attractors via Transformations

2015 ◽  
Vol 25 (10) ◽  
pp. 1530027 ◽  
Author(s):  
Xingxing Ai ◽  
Kehui Sun ◽  
Shaobo He ◽  
Huihai Wang
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Experimental Verification ◽  
Equilibrium Points ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
One Dimensional ◽  
Circular Grid

Three transformation approaches for generating grid multiscroll chaotic attractors are presented through theoretical analysis and numerical simulation. Three kinds of grid multiscroll chaotic attractors are generated based on one-dimensional multiscroll Chua system. The dynamics of the multiscroll chaotic attractors are analyzed by means of equilibrium points, eigenvalues, the largest Lyapunov exponent and complexity. As the experimental verification, we implemented the circular grid multiscroll attractor on DSP platform. The simulation and experimental results are consistent well with that of theoretical analysis, and it shows that the design approaches are effective.

A Switched Hyperchaotic System and Analysis of Dynamical Properties

2012 ◽  
Vol 452-453 ◽  
pp. 511-515
Author(s):  
Bian Li ◽  
Ai Xue Qi ◽  
Wei Bing Li
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Bifurcation Diagram ◽  
Experimental Results ◽  
Hyperchaotic System ◽  
Symbolic Function ◽  
Dynamical Properties ◽  
Lyapunov Exponent Spectrum

This paper introduces a new switched hyperchaotic system by utilizing symbolic function. The switched hyperchaotic system converts its states from one subsystem to another via symbolic functions. By the analysis of its dynamics, symmetry, dissipativity, Lyapunov exponent spectrum and bifurcation diagram of the system. The system is implemented by the FPGA hardware. It is shown that the experimental results are identical with numerical simulations, and the chaotic trajectories are much more complex.

Circuit Implementation of Multiscroll Chaotic Attractors Generated Using Step Function

2015 ◽  
Vol 25 (12) ◽  
pp. 1550160
Author(s):  
Yingjie Ma ◽  
Hua Jiang ◽  
Lei Ju
Keyword(s):  
Time Domain ◽  
Nonlinear Function ◽  
Step Function ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Time Domain ◽  
Hardware Circuit ◽  
The Physical Realization

A new chaotic system is proposed to generate multiscroll chaotic attractors. The major method used is for the step function to act as a nonlinear function. To prove that the proposed system can generate multiscroll chaotic attractors, the equilibrium point, the time domain waveform and the phase diagram of the proposed system are calculated. Finally, the design of the hardware circuit produces experimental results at a maximum of 8-scroll hardware. Theoretical analysis, simulation and hardware experimental results are fully matched, which further proves the existence of the proposed system and the physical realization. This provides the possibility for future applications in engineering.

CAN A THREE-DIMENSIONAL SMOOTH AUTONOMOUS QUADRATIC CHAOTIC SYSTEM GENERATE A SINGLE FOUR-SCROLL ATTRACTOR?

2004 ◽  
Vol 14 (04) ◽  
pp. 1395-1403 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Phase Space ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
System Parameters ◽  
New Chaotic System

Recently, we have investigated a new chaotic system of three-dimensional autonomous quadratic ordinary differential equations, and found that the system visually displays a four-scroll chaotic attractor confirmed by both numerical simulations and circuit implementation. In this paper, we further study the following question: Is it really true that this system can generate a four-scroll chaotic attractor, or is it only a numerical artifact? By a more careful theoretical analysis along with some further numerical simulations, we conclude that the four-scroll chaotic attractor of this system, which we observed on both computer and oscilloscope, cannot actually exist in theory. The fact is that this system has two co-existing two-scroll chaotic attractors that are arbitrarily close in the phase space for some system parameters, therefore extremely tiny numerical round-off errors or signal fluctuations will nudge the system orbit to switch from one attractor to another, thereby forming the seemingly single four-scroll chaotic attractor on screen display.

scholarly journals Analysis and electronic circuit implementation of an integer-and fractional-order Shimizu-Morioka system

2021 ◽  
Vol 67 (6 Nov-Dec) ◽  
Author(s):  
François Kapche Tagne ◽  
Guillaume Honoré KOM ◽  
Marceline Motchongom Tingue ◽  
Pierre Kisito Talla ◽  
V. Kamdoum Tamba
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Close Agreement ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Circuit Implementation ◽  
Bifurcation Structures ◽  
Electronic Circuit Implementation

The dynamics of an integer-order and fractional-order Lorenz like system called Shimizu-Morioka system is investigated in this paper. It is shown thatinteger-order Shimizu-Morioka system displays bistable chaotic attractors, monostable chaotic attractors and coexistence between bistable and monostable chaotic attractors. For suitable choose of parameters, the fractional-order Shimizu-Morioka system exhibits bistable chaotic attractors, monostable chaotic attractors, metastable chaos (i.e. transient chaos) and spiking oscillations. The bifurcation structures reveal that the fractional-order derivative affects considerably the dynamics of Shimizu-Morioka system. The chain fractance circuit is used to designand implement the integer- and fractional-order Shimizu-Morioka system in Pspice. A close agreement is observed between PSpice based circuit simulations and numerical simulations analysis. The results obtained in this work were not reported previously in the interger as well as in fractional-order Shimizu-Morioka system and thus represent an important contribution which may help us in better understanding of the dynamical behavior of this class of systems.

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