Theoretical analysis and circuit design of a novel high-dimensional hyperchaotic system

2014 ◽  
Author(s):  
Ling Liu ◽  
Yifan Liao
Keyword(s):  
Theoretical Analysis ◽  
Circuit Design ◽  
High Dimensional ◽  
Hyperchaotic System

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

Design-Oriented Analysis of Slow-Scale Bifurcations in Single Phase DC–AC Inverters via Autonomous Transformation Approach

2017 ◽  
Vol 27 (06) ◽  
pp. 1750086 ◽  
Author(s):  
Hao Zhang ◽  
Honghui Ding ◽  
Chuanzhi Yi
Keyword(s):  
Theoretical Analysis ◽  
Circuit Design ◽  
Single Phase ◽  
Underlying Mechanism ◽  
System Stability ◽  
Equivalent Model ◽  
Eigenvalue Sensitivity ◽  
Physical Experiments ◽  
Averaged Model ◽  
Theoretical Results

This paper deals with the design-oriented analysis of slow-scale bifurcations in single phase DC–AC inverters. Since DC–AC inverter belongs to a class of nonautonomous piecewise systems with periodic equilibrium orbits, the original averaged model has to be translated into an equivalent autonomous one via a virtual rotating coordinate transformation in order to simplify the theoretical analysis. Based on the virtual equivalent model, eigenvalue sensitivity is used to estimate the effect of the important parameters on the system stability. Furthermore, theoretical analysis is performed to identify slow-scale bifurcation behaviors by judging in what way the eigenvalue loci of the Jacobian matrix move under the variation of some important parameters. In particular, the underlying mechanism of the slow-scale unstable phenomenon is uncovered and discussed thoroughly. In addition, some behavior boundaries are given in the parameter space, which are suitable for optimizing the circuit design. Finally, physical experiments are performed to verify the above theoretical results.

Novel High-Precision Pitch Artifact Using Balls

2008 ◽  
Vol 381-382 ◽  
pp. 95-96 ◽  
Author(s):  
Masaharu Komori ◽  
Sonko Osawa ◽  
Osamu Sato ◽  
T. Kiten ◽  
D. Shirasaki ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
High Precision ◽  
Dimensional Accuracy ◽  
High Dimensional ◽  
Measuring Instruments ◽  
Order Accuracy ◽  
Special Process

In this research, a novel high-precision pitch artifact using balls is proposed for calibration of pitch measuring instruments. This pitch artifact is composed of the combination and the alignment of balls and cylinders on a plane. Balls, cylinders and planes are possible to be manufactured with several-ten-nanometer-order accuracy. Therefore, this artifact can accomplish high dimensional accuracy. In addition, manufacturing of this artifact is not difficult because time-consuming special process is not needed. In this report, the concept, structure and feature of this pitch artifact are proposed and theoretical analysis is carried out.

GENERATION AND IMPLEMENTATION OF HYPERCHAOTIC CHUA SYSTEM VIA STATE FEEDBACK CONTROL

2012 ◽  
Vol 22 (05) ◽  
pp. 1250119 ◽  
Author(s):  
HUILING XI ◽  
SIMIN YU ◽  
CHAOXIA ZHANG ◽  
YOULIN SUN
Keyword(s):  
Feedback Control ◽  
Theoretical Analysis ◽  
State Feedback ◽  
Piecewise Linear ◽  
State Feedback Control ◽  
Hyperchaotic System ◽  
Cubic Nonlinearity ◽  
State Equations ◽  
Dynamical Behaviors ◽  
Simulation Based

In this paper, a 4D hyperchaotic Chua system both with piecewise-linear nonlinearity and with smooth and piecewise smooth cubic nonlinearity is introduced, based on state feedback control. Dynamical behaviors of this hyperchaotic system are further investigated, including Lyapunov exponents spectrum, bifurcation diagram and solution of state equations. Theoretical analysis and numerical results show that this system can generate multiscroll hyperchaotic attractors. In addition, a circuit is designed for 4D hyperchaotic Chua system such that the double-scroll and 3-scroll hyperchaotic attractors can be physically obtained, demonstrating the effectiveness of the proposed simulation-based techniques.

A Novel Hyperchaotic System and its Circuit Implementation

2011 ◽  
Vol 467-469 ◽  
pp. 321-324
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponents ◽  
Circuit Design ◽  
Nonlinear Term ◽  
Fractal Dimensions ◽  
Hyperchaotic System ◽  
Circuit Implementation ◽  
Oscillator Circuit ◽  
Electronic Oscillator

A hyperchaotic system with only one nonlinear term is presented. The Lyapunov exponents, Lyapunov fractal dimensions, and phase diagram of this hyperchaotic system are obtained. Furthermore, one electronic oscillator circuit design of this hyperchaotic system is described using the Electronics Work Bench (EWB).

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

2008 ◽  
Vol 15 (04) ◽  
pp. 371-382 ◽  
Author(s):  
M. M. Al-sawalha ◽  
M. S. M. Noorani
Keyword(s):  
Theoretical Analysis ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
High Dimensional ◽  
Analysis Strategy ◽  
Relevant Variables ◽  
Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

PARTIAL STATE IMPULSIVE SYNCHRONIZATION OF A CLASS OF NONLINEAR SYSTEMS

2009 ◽  
Vol 19 (01) ◽  
pp. 387-393 ◽  
Author(s):  
YAN-WU WANG ◽  
CHANGYUN WEN ◽  
YENG CHAI SOH ◽  
ZHI-HONG GUAN
Keyword(s):  
Nonlinear System ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Hyperchaotic System ◽  
Impulsive Synchronization ◽  
Partial State ◽  
Simulation Results ◽  
System States ◽  
Synchronization Scheme

Impulsive synchronization of chaotic systems is an attractive topic and a number of interesting results have been obtained in recent years. However, all of these results on impulsive synchronization need to employ full states of the system to achieve the desired objectives. In this paper, impulsive synchronization that needs only part of system states is studied for a class of nonlinear system. Typical chaotic systems, such as Lorenz system, Chen's system, and a 4D hyperchaotic system, are taken as examples. A new scheme is proposed to select the impulsive intervals. After some theoretical analysis, simulation results show the effectiveness of the proposed synchronization scheme.

scholarly journals Hyperchaotic Circuit Based on Memristor Feedback with Multistability and Symmetries

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoyuan Wang ◽  
Xiaotao Min ◽  
Pengfei Zhou ◽  
Dongsheng Yu
Keyword(s):  
Theoretical Analysis ◽  
Dynamic Analysis ◽  
Chaotic System ◽  
Equilibrium Points ◽  
Experimental Results ◽  
System Dynamic ◽  
Hyperchaotic System ◽  
Analogue Circuits

A novel hyperchaotic circuit is proposed by introducing a memristor feedback in a simple Lorenz-like chaotic system. Dynamic analysis shows that it has infinite equilibrium points and multistability. Additionally, the symmetrical coexistent attractors are investigated. Further, the hyperchaotic system is implemented by analogue circuits. Corresponding experimental results are completely consistent with the theoretical analysis.

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