scholarly journals Symplectic Synchronization of Lorenz-Stenflo System with Uncertain Chaotic Parameters via Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Asymptotical Stability ◽  
Sufficient Condition ◽  
Null Solution ◽  
Special Cases ◽  
Error Dynamics

A new symplectic chaos synchronization of chaotic systems with uncertain chaotic parameters is studied. The traditional chaos synchronizations are special cases of the symplectic chaos synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics and a parameter difference. The symplectic chaos synchronization with uncertain chaotic parameters may be applied to the design of secure communication systems. Finally, numerical results are studied for symplectic chaos synchronized from two identical Lorenz-Stenflo systems in three different cases.

scholarly journals Enhanced Symplectic Synchronization between Two Different Complex Chaotic Systems with Uncertain Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Numerical Simulations ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Asymptotical Stability ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Null Solution ◽  
Special Cases ◽  
Error Dynamics ◽  
Complex Chaotic Systems

An enhanced symplectic synchronization of complex chaotic systems with uncertain parameters is studied. The traditional chaos synchronizations are special cases of the enhanced symplectic synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics. The enhanced symplectic synchronization may be applied to the design of secure communication. Finally, numerical simulations results are performed to verify and illustrate the analytical results.

An Adaptive Chaos Synchronization with Controller and Secure Communication

2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Sufficient Condition ◽  
Control Parameters

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.

FUZZY CHAOS SYNCHRONIZATION VIA SAMPLED DRIVING SIGNALS

2004 ◽  
Vol 14 (08) ◽  
pp. 2721-2733 ◽  
Author(s):  
JUAN GONZALO BARAJAS-RAMÍREZ ◽  
GUANRONG CHEN ◽  
LEANG S. SHIEH
Keyword(s):  
Continuous Time ◽  
System Approach ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Disturbance Attenuation ◽  
Fuzzy Observer ◽  
Master System ◽  
Error Dynamics ◽  
Takagi Sugeno ◽  
Driving Signal

In this paper, a methodology to design a system that robustly synchronizes a master chaotic system from a sampled driving signal is developed. The method is based on the fuzzy Takagi–Sugeno representation of chaotic systems, from which a continuous-time fuzzy observer is designed as the solution of an LMI minimization problem such that the error dynamics have H∞disturbance attenuation performance. Then, from the dual-system approach, the fuzzy observer is digitally redesigned such that the performance is maintained for the sampled master system. The effectiveness of the proposed synchronization methodology is finally illustrated via numerical simulations of the chaotic Chen's system.

scholarly journals DII-Based Linear Feedback Control Design for Practical Synchronization of Chaotic Systems with Uncertain Input Nonlinearity and Application to Secure Communication

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Exponential Convergence ◽  
Chaotic Synchronization ◽  
Linear Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Input Nonlinearity ◽  
Uncertain Input

The concept of practical synchronization is introduced and the chaos synchronization of master-slave chaotic systems with uncertain input nonlinearities is investigated. Based on the differential and integral inequalities (DII) approach, a simple linear control is proposed to realize practical synchronization for master-slave chaotic systems with uncertain input nonlinearities. Besides, the guaranteed exponential convergence rate can be prespecified. Applications of proposed master-slave chaotic synchronization technique to secure communication as well as several numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained result.

A SIMPLE WAY TO SYNCHRONIZE CHAOTIC SYSTEMS WITH APPLICATIONS TO SECURE COMMUNICATION SYSTEMS

1993 ◽  
Vol 03 (06) ◽  
pp. 1619-1627 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Lyapunov Exponents ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Functional Form ◽  
Response System ◽  
Definition Of

In this paper, we provide a scheme for synthesizing synchronized circuits and systems. Synchronization of the drive and response system is proved trivially without the need for computing numerically the conditional Lyapunov exponents. We give a definition of the driving and response system having the same functional form, which is more general than the concept of homogeneous driving by Pecora & Carroll [1991]. Finally, we show how synchronization coupled with chaos can be used to implement secure communication systems. This is illustrated with examples of secure communication systems which are inherently error-free in contrast to the signal-masking schemes proposed in Cuomo & Oppenheim [1993a,b] and Kocarev et al. [1992].

scholarly journals Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1= 0.0395,L2= 0 and L3= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

scholarly journals Lag Synchronization of Coupled Multidelay Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Luo Qun ◽  
Peng Hai-Peng ◽  
Xu Ling-Yu ◽  
Yang Yi Xian
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Theory ◽  
Sufficient Condition ◽  
Improved Method ◽  
Lag Synchronization

Chaos synchronization is an active topic, and its possible applications have been studied extensively. In this paper we present an improved method for lag synchronization of chaotic systems with coupled multidelay. The Lyapunov theory is used to consider the sufficient condition for synchronization. The specific examples will demonstrate and verify the effectiveness of the proposed approach.

OBSERVER-BASED SYNCHRONIZATION FOR A CLASS OF FRACTIONAL CHAOTIC SYSTEMS VIA A SCALAR SIGNAL: RESULTS INVOLVING THE EXACT SOLUTION OF THE ERROR DYNAMICS

2011 ◽  
Vol 21 (03) ◽  
pp. 955-962 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Exact Analytical Solution ◽  
Fractional Order Systems ◽  
Fractional Error ◽  
Transmitted Signal ◽  
Error Dynamics

This paper deals with chaos synchronization for a class of fractional-order systems characterized by one nonlinearity. In particular, an observer-based approach is illustrated, which presents two remarkable features: (i) it provides an exact analytical solution of the fractional error dynamics, written in terms of Mittag-Leffler function; (ii) it enables synchronization to be achieved using a scalar transmitted signal. Finally, a synchronization example based on fractional Chua's system is illustrated, with the aim to show the capabilities of the developed approach.

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

2016 ◽  
Vol 40 (4) ◽  
pp. 1177-1187 ◽  
Author(s):  
Hua Wang ◽  
Jian-Min Ye ◽  
Zhong–Hua Miao ◽  
Edmond A Jonckheere
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Finite Time ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Uncertain Parameters ◽  
Wide Range ◽  
Zero Items

This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

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