Synchronization through Compound Chaotic Signal in Chua's Circuit and Murali–Lakshmanan–Chua Circuit

1997 ◽  
Vol 07 (02) ◽  
pp. 415-421 ◽  
Author(s):  
K. Murali ◽  
M. Lakshmanan
Keyword(s):  
Feedback Loop ◽  
Chaotic Systems ◽  
Chaotic Signal ◽  
Drive System ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Response System ◽  
Chua Circuit ◽  
Response Systems ◽  
System Variables

In this letter the idea of synchronization of chaotic systems is further extended to the case where all the drive system variables are combined to obtain a compound chaotic drive signal. An appropriate feedback loop is constructed in the response system to achieve synchronization among the variables of drive and response systems. We apply this method of synchronization to the familiar Chua's circuit and Murali–Lakshmanan–Chua circuit equations.

EXPERIMENTAL MODIFICATIONS OF VOA-BASED AUTONOMOUS AND NONAUTONOMOUS CHUA'S CIRCUITS FOR HIGHER DIMENSIONAL OPERATION

2006 ◽  
Vol 16 (09) ◽  
pp. 2649-2658
Author(s):  
RECAI KILIÇ
Keyword(s):  
Experimental Method ◽  
Operational Amplifier ◽  
Experimental Results ◽  
High Dimensional ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Voltage Mode ◽  
Pspice Simulation ◽  
Chua Circuit ◽  
Higher Dimensional

In order to operate in higher dimensional form of autonomous and nonautonomous Chua's circuits keeping their original chaotic behaviors, we have experimentally modified VOA (Voltage Mode Operational Amplifier)-based autonomous Chua's circuit and nonautonomous MLC [Murali–Lakshmanan–Chua] circuit by using a simple experimental method. After introducing this experimental method, we will present PSpice simulation and experimental results of modified high dimensional autonomous and nonautonomous Chua's circuits.

Synchronization of Continuous Scalar Chaotic Signal from Uncertain Chaotic System

2013 ◽  
Vol 816-817 ◽  
pp. 843-846
Author(s):  
Jing Wang ◽  
Hui Zhong
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Chaotic Systems ◽  
System Simulation ◽  
Chaotic Signal ◽  
Response System ◽  
Synchronization Scheme

This paper presents the synchronizing problem of scalar chaotic signal. A class of nonlinear chaotic systems is discussed which has unknown part in model. The proposed approach is based on canonical form of the response system. Simulation result shows the effectiveness of our synchronization scheme.

LINEAR AND NONLINEAR GENERALIZED SYNCHRONIZATION OF CHAOTIC SYSTEMS

2010 ◽  
Vol 24 (31) ◽  
pp. 6143-6155
Author(s):  
XING-YUAN WANG ◽  
JING ZHANG
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
State Observer ◽  
Drive System ◽  
Generalized Synchronization ◽  
Response System ◽  
Linear And Nonlinear ◽  
Synchronization Scheme ◽  
Application Scope

In this paper, the linear and nonlinear generalized synchronization of chaotic systems is investigated. Based on the modified state observer method, a new synchronization approach is proposed with more extensive application scope. The proposed synchronization scheme can realize the linear and nonlinear generalized synchronizations of same dimensional or different dimensional chaotic systems. Sufficient conditions of global asymptotic generalized synchronization between the drive system and the response system are gained on the basis of the state observer theory. Numerical simulations further illustrate the effectiveness of the proposed scheme.

Detecting Weak Signals by Using Memristor-Involved Chua’s Circuit and Verification in Experimental Platform

2020 ◽  
Vol 30 (13) ◽  
pp. 2050193
Author(s):  
Li Xiong ◽  
Xinguo Zhang ◽  
Sufen Teng ◽  
Liwan Qi ◽  
Peijin Zhang
Keyword(s):  
Comparative Research ◽  
Chaotic Systems ◽  
Short Circuit ◽  
Characteristic Curve ◽  
Detection Methods ◽  
Measurement Unit ◽  
Chua’S Circuit ◽  
Weak Signals ◽  
Chua's Circuit ◽  
Research Platform

Since the traditional detection methods cannot accurately detect, determine and extract weak signals, the extreme sensitivity of chaotic systems to initial values is used for weak signal detection using a memristor-based chaotic system. Then, in order to find out all kinds of static nonlinear circuits suitable for Chua’s circuit with identical parameters, a comparative research platform is designed to generate five kinds of nonlinearity by taking advantage of the active short-circuit line method using the memristor-involved chaotic Chua’s circuit. The comparative research platform consists of three parts: a linear circuit unit, multiple nonlinear static function circuits and a nonlinear characteristic curve measurement unit connected by an electronic switch. By pressing the space bar, the switch between the active short-circuit line and the physical short-circuit line can be realized. The diffeomorphism between them is proved by comparing the memristive nonlinearity shape and the trilinear amplitude limiting the nonlinearity in the chaotic systems. Accordingly, hardware circuit experiments are carried out to verify the effectiveness and feasibility of the comparative research platform with various nonlinearity for Chua’s circuit. A good agreement is shown between the numerical simulations and the experimental results.

EXPERIMENTAL CHAOS SYNCHRONIZATION IN CHUA'S CIRCUIT

1992 ◽  
Vol 02 (03) ◽  
pp. 705-708 ◽  
Author(s):  
LEON O. CHUA ◽  
LJUPCO KOCAREV ◽  
KEVIN ECKERT ◽  
MAKOTO ITOH
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Chua’S Circuit ◽  
Chua's Circuit

Several recent papers have investigated the feasibility of synchronization of chaotic systems. Experimentally one of the easiest systems to control and synchronize is the electronic circuit. This paper examines synchronization in Chua's Circuit, proven to be the simplest electronic circuit to exhibit chaotic behavior.

ROBUST DEAD-BEAT SYNCHRONIZATION AND COMMUNICATION FOR DISCRETE-TIME CHAOTIC SYSTEMS

2002 ◽  
Vol 12 (04) ◽  
pp. 835-846 ◽  
Author(s):  
KUANG-YOW LIAN ◽  
PETER LIU ◽  
CHIAN-SONG CHIU ◽  
TUNG-SHENG CHIANG
Keyword(s):  
Numerical Simulations ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Chaotic Systems ◽  
Performance Criterion ◽  
Drive System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chaotic Communication ◽  
Response System

This paper proposes synchronization and chaotic communication for a class of Lur'e type discrete-time chaotic systems. The scalar outputs are suitably chosen in a flexible manner to be linear, nonlinear, or predictive, and along with the drive system are then written in an output injection form. Then with a suitable design of an observer-based response system, dead-beat performance is achieved for synchronization and chaotic communications. Then disturbances in the drive system are considered. Using an ℋ∞performance criterion, the disturbance is attenuated to a prescribed level by solving linear matrix inequalities (LMIs). Numerical simulations are carried out to verify the dead-beat performance.

CONTROLLING CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 139-149 ◽  
Author(s):  
GUANRONG CHEN ◽  
XIAONING DONG
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Control Process ◽  
Periodic Signal ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Simulation Results ◽  
Feedback Control Strategy

The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the well-known Chua's circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. Simple sufficient conditions for the controllability of this particular circuit are established. Simulation results are included to visualize the control process. A circuit implementation of the designed feedback control is realized by adding a linear resistor and an appropriate periodic-signal generator to the original circuit.

GENERATION OF n × m-SCROLL ATTRACTORS UNDER A CHUA-CIRCUIT FRAMEWORK

2007 ◽  
Vol 17 (11) ◽  
pp. 3951-3964 ◽  
Author(s):  
SIMIN YU ◽  
WALLACE K. S. TANG ◽  
G. CHEN
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chua’S Circuit ◽  
Electronic Circuits ◽  
Third Order ◽  
Chua's Circuit ◽  
Chua Circuit ◽  
Dynamical Behaviors ◽  
First Time

In this paper, the generation of n × m-scroll attractors under a Chua-circuit framework is presented. By using a sawtooth function, f1(x), and a staircase function, f2(y), n × m-scroll attractors can be generated and observed from a third-order circuit. Its dynamical behaviors are investigated by means of theoretical analysis as well as numerical simulation. Moreover, two electronic circuits are designed for its realization, and experimental observations of n × m-scroll attractors based on Chua's circuit are reported, for the first time in the literature.

CONTROLLING CHAOTIC DYNAMICS USING BACKSTEPPING DESIGN WITH APPLICATION TO THE LORENZ SYSTEM AND CHUA'S CIRCUIT

1999 ◽  
Vol 09 (07) ◽  
pp. 1425-1434 ◽  
Author(s):  
SAVERIO MASCOLO ◽  
GIUSEPPE GRASSI
Keyword(s):  
Steady State ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Backstepping Design ◽  
Chua’S Circuit ◽  
General Applicability ◽  
Recursive Procedure ◽  
Chua's Circuit ◽  
The Lorenz System

In this Letter backstepping design is proposed for controlling chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The advantages of the method are the following: (i) it represents a systematic procedure for controlling chaotic or hyperchaotic dynamics; (ii) it can be applied to several circuits and systems reported in literature; (iii) stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory can be achieved. In order to illustrate the general applicability of backstepping design, the tool is utilized for controlling the chaotic dynamics of the Lorenz system and Chua's circuit. Finally, numerical simulations are carried out to show the effectiveness of the technique.

EXPERIMENTAL DEMONSTRATION OF SECURE COMMUNICATIONS VIA CHAOTIC SYNCHRONIZATION

1992 ◽  
Vol 02 (03) ◽  
pp. 709-713 ◽  
Author(s):  
Lj. KOCAREV ◽  
K. S. HALLE ◽  
K. ECKERT ◽  
L. O. CHUA ◽  
U. PARLITZ
Keyword(s):  
Recovery Process ◽  
Chaotic Signal ◽  
Chaotic Synchronization ◽  
Secure Communications ◽  
Chua’S Circuit ◽  
Experimental Demonstration ◽  
Chua's Circuit

Secure communications via chaotic synchronization is experimentally demonstrated using Chua's circuit. In our experiment the energy lost in the information-bearing signal is approximately 0.6 dBV. The reduction in chaotic signal after the recovery process is between -40 and -50 dBV.

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