Chaos synchronization of Chua's circuit and Lorenz system based on strictly positive realness

2014 ◽  
Author(s):  
Hong Niu ◽  
Guoshan Zhang ◽  
Jiankui Wang
Keyword(s):  
Chaos Synchronization ◽  
Lorenz System ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Positive Realness ◽  
Strictly Positive Realness

CHAOTIC DYNAMICS AND SYNCHRONIZATION OF FRACTIONAL-ORDER CHUA'S CIRCUITS WITH A PIECEWISE-LINEAR NONLINEARITY

2005 ◽  
Vol 19 (20) ◽  
pp. 3249-3259 ◽  
Author(s):  
JUN GUO LU
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Piecewise Linear ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Synchronization Method ◽  
Simulation Results

In this paper, we numerically investigate the chaotic behaviors of the fractional-order Chua's circuit with a piecewise-linear nonlinearity. We find that chaos exists in the fractional-order Chua's circuit with order less than 3. The lowest order we find to have chaos is 2.7 in the homogeneous fractional-order Chua's circuit and 2.8 in the unhomogeneous fractional-order Chua's circuit. Our results are validated by the existence of a positive Lyapunov exponent. A chaos synchronization method is also presented for synchronizing the homogeneous fractional-order chaotic Chua's systems. The approach, based on stability theory of fractional-order linear systems, is simple and theoretically rigorous. It does not require the computation of the conditional Lyapunov exponents. Simulation results are used to visualize and illustrate the effectiveness of the proposed synchronization method.

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.

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.

CHAOS SYNCHRONIZATION IN SC-CNN-BASED CIRCUIT AND AN INTERESTING INVESTIGATION: CAN A SC-CNN-BASED CIRCUIT BEHAVE SYNCHRONOUSLY WITH THE ORIGINAL CHUA'S CIRCUIT?

2004 ◽  
Vol 14 (03) ◽  
pp. 1071-1083 ◽  
Author(s):  
RECAI KILIÇ
Keyword(s):  
Chaos Synchronization ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Pspice Simulation ◽  
Synchronization Phenomenon ◽  
Simulation Results

In this work, after giving a complete verification of the continuous synchronization between two identical SC-CNN-based circuits depending on the driving variable, we have investigated the continuous synchronization phenomenon between SC-CNN-based circuit and Chua's circuit. PSpice simulation results confirm that SC-CNN-based circuit can behave synchronously with Chua's circuit in the case when very accurate parameter equalities are provided.

TWO IMPULSIVE SYNCHRONIZATION STUDIES USING SC-CNN-BASED CIRCUIT AND CHUA'S CIRCUIT

2004 ◽  
Vol 14 (09) ◽  
pp. 3277-3293 ◽  
Author(s):  
RECAI KILIÇ ◽  
MUSTAFA ALÇI ◽  
ENIS GÜNAY
Keyword(s):  
Dynamical Systems ◽  
Lorenz System ◽  
Chua’S Circuit ◽  
Cell Dynamics ◽  
Chua's Circuit ◽  
Pspice Simulation ◽  
Impulsive Synchronization ◽  
Hardware Implementations ◽  
Chaotic Circuits ◽  
Simulation Results

The impulsive synchronization method has been applied to several well-known chaotic circuits and systems such as Chua's circuit, Lorenz system and hyperchaotic circuit in the literature. In this paper, we also present two impulsive synchronization studies using SC-CNN-based circuit and Chua's circuit. In the first study, we have investigated the impulsive synchronization between two SC-CNN-based circuits. Pspice simulation results show that two SC-CNN-based circuits can be synchronized impulsively via x1 and x2 cell dynamics for different impulse width and impulse period values. And in the second study, we have investigated the impulsive synchronization between SC-CNN-based circuit and Chua's circuit. Pspice simulation results verify that two chaotic circuits, which have identical dynamical systems via appropriate parameter transformations but having quite different hardware implementations, can be synchronized impulsively for different impulse width and impulse period values.

CHAOS SYNCHRONIZATION IN CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 93-108 ◽  
Author(s):  
LEON O. CHUA ◽  
MAKOTO ITOH ◽  
LJUPCO KOCAREV ◽  
KEVIN ECKERT
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Behavior ◽  
Chua’S Circuit ◽  
Chua's Circuit

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.

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