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.

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Hadi Delavari ◽  
Danial Senejohnny ◽  
Dumitru Baleanu
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Canonical Form ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Synchronization ◽  
Mode Theory ◽  
Synchronization Scheme

AbstractIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

Matrix Projective Synchronization of Chaotic Systems and the Application in Secure Communication

2014 ◽  
Vol 644-650 ◽  
pp. 4216-4220
Author(s):  
Feng Liu
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Chaotic Signal ◽  
Projective Synchronization ◽  
Information Signal ◽  
Simulation Results

First of all, we investigate adaptive matrix projective synchronization of the chaotic system. Finally, this method is applied to secure communication through improved chaotic masking. The information signal is mixed with the chaotic signal before being transmitted, and is recovered without distortion through the synchronized receiver. Simulation results show that the scheme has a good performance.

Seven Dimension Chaotic System and its Circuit Implementation

2012 ◽  
Vol 588-589 ◽  
pp. 1251-1254 ◽  
Author(s):  
Jian Liang Zhu ◽  
Chun Yu Yu
Keyword(s):  
Chaotic System ◽  
Chaotic Behavior ◽  
Circuit Simulation ◽  
System Simulation ◽  
Chaotic Signal ◽  
Chaotic Attractors ◽  
Signal Source ◽  
Circuit Implementation ◽  
Practical Application ◽  
Signal Encryption

In order to generate more complex chaotic attractors, a seven-dimensional chaotic system is constructed, and relevant chaotic attractors can be obtained by Matlab numerical simulation. Lyapunov exponents validate that the system is chaotic. 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. Chaotic behavior of the system is proved farther. A new chaotic signal source is provided for practical application based on chaos such as secrecy communication and signal encryption fields.

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.

SYNCHRONIZATION THEOREM FOR A CHAOTIC SYSTEM

1995 ◽  
Vol 05 (01) ◽  
pp. 297-302 ◽  
Author(s):  
JÖRG SCHWEIZER ◽  
MICHAEL PETER KENNEDY ◽  
MARTIN HASLER ◽  
HERVÉ DEDIEU
Keyword(s):  
Lyapunov Function ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Secure Communications ◽  
Error Feedback ◽  
Response System ◽  
Synchronization Method

Since Pecora & Carroll [Pecora & Carroll, 1991; Carroll & Pecora, 1991] have shown that it is possible to synchronize chaotic systems by means of a drive-response partition of the systems, various authors have proposed synchronization schemes and possible secure communications applications [Dedieu et al., 1993, Oppenheim et al., 1992]. In most cases synchronization is proven by numerically computing the conditional Lyapunov exponents of the response system. In this work a new synchronization method using error-feedback is developed, where synchronization is provable using a global Lyapunov function. Furthermore, it is shown how this scheme can be applied to secure communication systems.

Hidden Chaotic Attractors and Synchronization for a New Fractional-Order Chaotic System

2019 ◽  
Vol 14 (8) ◽  
Author(s):  
Zuoxun Wang ◽  
Jiaxun Liu ◽  
Fangfang Zhang ◽  
Sen Leng
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Chaotic Attractors ◽  
Finite Time Stability ◽  
Integer Order ◽  
Different Types ◽  
Synchronization Scheme

Although a large number of hidden chaotic attractors have been studied in recent years, most studies only refer to integer-order chaotic systems and neglect the relationships among chaotic attractors. In this paper, we first extend LE1 of sprott from integer-order chaotic systems to fractional-order chaotic systems, and we add two constant controllers which could produce a novel fractional-order chaotic system with hidden chaotic attractors. Second, we discuss its complicated dynamic characteristics with the help of projection pictures and bifurcation diagrams. The new fractional-order chaotic system can exhibit self-excited attractor and three different types of hidden attractors. Moreover, based on fractional-order finite time stability theory, we design finite time synchronization scheme of this new system. And combination synchronization of three fractional-order chaotic systems with hidden chaotic attractors is also derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization methods.

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.

scholarly journals Transformation of the generalized chaotic system into canonical form

2017 ◽  
Vol 3 (3) ◽  
pp. 117
Author(s):  
Roman Voliansky
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Discrete Model ◽  
Control Algorithm ◽  
Chaotic Systems ◽  
Numerical Algorithms ◽  
Chaotic Attractors ◽  
Output Variable ◽  
State Spaces ◽  
Sample Time

The paper deals with the developing of the numerical algorithms for transformation of generalized chaotic system into canonical form. Such transformation allows us to simplify control algorithm for chaotic system. These algorithms are defined by using Lie derivatives for output variable and solution of nonlinear equations. Usage of proposed algorithm is one of the ways for discovering of new chaotic attractors. These attractors can be obtained by transformation of known chaotic systems into various state spaces. Transformed attractors depend on both parameters of chaotic system and sample time of its discrete model.

scholarly journals FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
J. Perez-Padron ◽  
C. Posadas-Castillo ◽  
J. Paz-Perez ◽  
E. Zambrano-Serrano ◽  
M. A. Platas-Garza
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Tracking Error ◽  
Control Law ◽  
Trajectory Tracking Control ◽  
Field Programmable ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

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