HYBRID CHAOS SYNCHRONIZATION

2003 ◽  
Vol 13 (05) ◽  
pp. 1197-1216 ◽  
Author(s):  
JUAN-GONZALO BARAJAS-RAMÍREZ ◽  
GUANRONG CHEN ◽  
LEANG S. SHIEH

The problem of hybrid chaos synchronization is investigated, where a digital response subsystem is designed to synchronize with an analog drive subsystem. The approach taken is a new prediction-based digital redesign for a continuous-time observer embedded in the response via an optimal linearization approach of the nonlinear chaotic systems. Three typical but topologically quite different chaotic systems, Chua's circuit, Duffing oscillator, and Chen's system, are simulated thereby validating the novel design proposed in this paper.

1992 ◽  
Vol 02 (03) ◽  
pp. 705-708 ◽  
Author(s):  
LEON O. CHUA ◽  
LJUPCO KOCAREV ◽  
KEVIN ECKERT ◽  
MAKOTO ITOH

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.


1993 ◽  
Vol 03 (01) ◽  
pp. 93-108 ◽  
Author(s):  
LEON O. CHUA ◽  
MAKOTO ITOH ◽  
LJUPCO KOCAREV ◽  
KEVIN ECKERT

A number of recent papers have investigated the feasibility of synchronizing 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.


2002 ◽  
Vol 12 (10) ◽  
pp. 2239-2253 ◽  
Author(s):  
GUO-PING JIANG ◽  
WALLACE K. S. TANG

Based on Lyapunov stabilization theory, this paper proposes a new generic criterion of global chaos synchronization between two coupled chaotic systems from a unidirectional linear error feedback coupling approach. The criterion is successfully applied to some typical chaotic systems with different types of nonlinearity, such as the classic Chua's circuit, the modified Chua's circuit with a sine function, and the Rössler and Lorenz chaotic systems. The coupling parameters are determined according to the new criterion so as to ensure the coupled systems' global chaos synchronization.


2004 ◽  
Vol 14 (08) ◽  
pp. 2721-2733 ◽  
Author(s):  
JUAN GONZALO BARAJAS-RAMÍREZ ◽  
GUANRONG CHEN ◽  
LEANG S. SHIEH

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.


2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos

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.


2005 ◽  
Vol 15 (08) ◽  
pp. 2433-2455
Author(s):  
JOSE I. CANELON ◽  
LEANG S. SHIEH ◽  
SHU M. GUO ◽  
HEIDAR A. MALKI

This paper presents a neural network-based digital redesign approach for digital control of continuous-time chaotic systems with unknown structures and parameters. Important features of the method are that: (i) it generalizes the existing optimal linearization approach for the class of state-space models which are nonlinear in the state but linear in the input, to models which are nonlinear in both the state and the input; (ii) it develops a neural network-based universal optimal linear state-space model for unknown chaotic systems; (iii) it develops an anti-digital redesign approach for indirectly estimating an analog control law from a fast-rate digital control law without utilizing the analog models. The estimated analog control law is then converted to a slow-rate digital control law via the prediction-based digital redesign method; (iv) it develops a linear time-varying piecewise-constant low-gain tracker which can be implemented using microprocessors. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology.


2020 ◽  
Vol 30 (13) ◽  
pp. 2050193
Author(s):  
Li Xiong ◽  
Xinguo Zhang ◽  
Sufen Teng ◽  
Liwan Qi ◽  
Peijin Zhang

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.


1993 ◽  
Vol 03 (04) ◽  
pp. 1057-1066 ◽  
Author(s):  
K. MURALI ◽  
M. LAKSHMANAN

In this paper, we report the numerical observations of synchronization in driven Chua's circuit using the criterion of Pecora and Carroll. Also, synchronization behavior of this system is investigated under the influence of Gaussian noise signal and we point out that it is possible to obtain synchronization even in this environment. More interestingly, we also point out the novel possibility of controlling unsynchronized motion using the adaptive control algorithm.


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