A New Grid Multi-Scroll Chaotic System and the Simulation Based on Labview

2012 ◽  
Vol 538-541 ◽  
pp. 2666-2669
Author(s):  
Yong Huang
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Step Function ◽  
Simulation System ◽  
Unstable System ◽  
Simulation Based ◽  
Two Parameters ◽  
The Way

In order to get the grid Multi-Scroll in the two directions, based on a simple unstable system, the way of the combination of the translational transform and step function was put forward to make the scrolls extending in the x and y directions in this paper. The quantity of scrolls can be controlled by two parameters N and M. A simulation system was designed with Labview to simulate grid Multi-Scroll chaotic system, it demonstrates the existence of grid Multi-Scroll chaotic attractor.

scholarly journals A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

SHIL'NIKOV HETEROCLINIC ORBITS IN A CHAOTIC SYSTEM

2007 ◽  
Vol 21 (25) ◽  
pp. 4429-4436 ◽  
Author(s):  
FENG-YUN SUN
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Heteroclinic Orbits ◽  
Geometric Structures ◽  
Undetermined Coefficient ◽  
Coefficient Method ◽  
Undetermined Coefficient Method

In this paper, a chaotic system which exhibits a chaotic attractor with only three equilibria for some parameters is considered. The existence of heteroclinic orbits of the Shil'nikov type in a chaotic system has been proved using the undetermined coefficient method. As a result, the Shil'nikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of the attractor are determined by these heteroclinic orbits.

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.

scholarly journals Simulated patient contributions to enhancing exercise physiology student clinical assessment skills

2019 ◽  
Vol 4 (S1) ◽  
Author(s):  
Nathan E. Reeves ◽  
Monique C. Waite ◽  
Neil Tuttle ◽  
Andrea Bialocerkowski
Keyword(s):  
Repeated Measures ◽  
Clinical Skills ◽  
Exercise Physiology ◽  
History Taking ◽  
Learning Modules ◽  
Motivation For Learning ◽  
Preparedness For Practice ◽  
Simulation Based ◽  
Two Parameters ◽  
Physiology Students

Abstract Background The aim of this study was to evaluate exercise physiology students’ perceptions of two simulation-based learning modules focused on communication and interpersonal skills during history taking. Methods A prospective, repeated-measures cohort study was conducted with 15 participants. The study evaluated two simulation-based learning modules in a 1-year Graduate Diploma of Exercise Science program. Surveys were administered at four time points: prior to each module and following each module. Students rated their confidence in communication and history taking, and perception of preparedness for practice, motivation for learning, and benefits of undertaking simulation-based learning. Quantitative data were analyzed descriptively and by using repeated measures tests. Qualitative data underwent thematic analyses. Results Students reported a significant improvement in their confidence in communication (P = 0.043) and in two parameters related to history taking (P = 0.034 and 0.035) following the completion of the two modules. There was 96% agreement that the simulation-based learning better prepared students for practice as an exercise physiologist. Significant changes occurred in all aspects of motivation for learning (P ranging from < 0.001 to 0.036) except for usefulness, where there was a ceiling effect (medians of 7 on a 7-point scale). Qualitative analysis demonstrated benefit to participants around themes of experiential learning, realism, opportunity to develop clinical skills, and debriefing. Students also made suggestions with respect to the activity structure of the simulation-based learning modules. Conclusions The results of this study indicated that simulation-based learning employing SPs increased the confidence and preparedness of exercise physiology students for conducting history taking, a requisite exercise physiology skill. Future studies should include behavioral measures of skill attainment and include follow-up evaluation to appraise the application of these skills into clinical practice.

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 Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 564 ◽  
Author(s):  
Jesus Munoz-Pacheco ◽  
Ernesto Zambrano-Serrano ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Equilibrium System ◽  
Hidden Attractors ◽  
Hidden Chaotic Attractor

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

scholarly journals A Multiscroll Chaotic Attractors with Arrangement of Saddle-Shapes and Its Field Programmable Gate Array (FPGA) Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Faqiang Wang ◽  
Yufang Xiao
Keyword(s):  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Equilibrium Points ◽  
Research Result ◽  
Step Function ◽  
Phase Locked Loops ◽  
Chaotic Attractors ◽  
Digital To Analog Converter ◽  
Field Programmable ◽  
Gate Array

Based on the step function and signum function, a chaotic system which can generate multiscroll chaotic attractors with arrangement of saddle-shapes is proposed and the stability of its equilibrium points is analyzed. The under mechanism for the generation of multiscroll chaotic attractors and the reason for the arrangement of saddle shapes and being symmetric about y-axis are presented, and the rule for controlling the number of scroll chaotic attractors with saddle shapes is designed. Based on the core chips including Altera Cyclone IV EP4CE10F17C8 Field Programmable Gate Array and Digital to Analog Converter chip AD9767, the peripheral circuit and the Verilog Hardware Description Language program for realization of the proposed multiscroll chaotic system is constructed and some experimental results are presented for confirmation. The research result shows that the occupation of multipliers and Phase-Locked Loops in Field Programmable Gate Array is zero.

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.

THE SCROLL CONTROL AND IMPROVING CASCADE SYNCHRONIZATION OF A NOVEL CHAOTIC SYSTEM

2014 ◽  
Vol 28 (08) ◽  
pp. 1450058 ◽  
Author(s):  
YIN LI ◽  
YULIN ZHAO ◽  
ZHENG-AN YAO
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Numerical Results ◽  
Cascade Method ◽  
New System

In this paper, on the basis of the Laypunov stability and the cascade synchronization approach, an effectual scroll controller and improving cascade synchronization approach are derived. The chaotic attractor can be displayed to be lopsided, till to be 1-scroll and periodic via the different scroll controller. And the proposed synchronization technique is applied to the new system, which the synchronization controller obtained by improving cascade method and adaptive functions. Numerical results are used to verify the effectiveness of the scheme.

A PICTURE BOOK OF TWO FAMILIES OF CUBIC MAPS

1993 ◽  
Vol 04 (03) ◽  
pp. 553-568 ◽  
Author(s):  
FERNANDO CABRAL ◽  
ALEXANDRE LAGO ◽  
JASON A. C. GALLAS
Keyword(s):  
Dynamical Systems ◽  
High Resolution ◽  
Parameter Space ◽  
Picture Book ◽  
Initial Conditions ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Two Parameters ◽  
The Way

This paper reports high-resolution isoperiodic diagrams for two model-families of dynamical systems characterised by one-dimensional maps depending on two parameters. We present a comparison of both diagrams, investigating the way in which initial conditions affect isoperiodic sets in the parameter space of both systems and the similarities between them. Although both models represent quite different dynamical systems, they are found to have many properties in common in their space of parameters.

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