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.

IMPULSIVE SYNCHRONIZATION BETWEEN TWO MIXED-MODE CHAOTIC CIRCUITS

2005 ◽  
Vol 14 (02) ◽  
pp. 333-346 ◽  
Author(s):  
RECAİ KILIÇ
Keyword(s):  
Mixed Mode ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Minimum Length ◽  
Chua’S Circuit ◽  
Chaotic Circuit ◽  
Chua's Circuit ◽  
Impulsive Synchronization ◽  
Synchronization Method ◽  
Chaotic Circuits

So far, impulsive synchronization method has been applied to several well-known chaotic circuits and systems such as Chua's circuit, Lorenz system and hyperchaotic circuit. Here, we present a study of impulsive synchronization of another chaotic circuit, namely mixed-mode chaotic circuit which oscillates both autonomous and nonautonomous chaotic dynamics. By choosing two mixed-mode chaotic circuits as driving and driven chaotic circuits, we investigated whether these circuits are synchronized impulsively or not by evaluating the minimum length of impulse width (Q), and the ratio of impulse width to impulse period (Q/T). The results of our investigation confirm that two mixed-mode chaotic circuits can be synchronized impulsively with very narrow impulse width.

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.

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.

SET STABILIZATION OF A MODIFIED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (02) ◽  
pp. 567-604 ◽  
Author(s):  
SHIHUA LI ◽  
YU-PING TIAN
Keyword(s):  
Equilibrium Point ◽  
Lyapunov Stability ◽  
Closed Loop ◽  
Invariant Set ◽  
Linear Feedback ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Linear Feedback Controller ◽  
Simulation Results ◽  
First Time

In this paper, we develop a simple linear feedback controller, which employs only one of the states of the system, to stabilize the modified Chua's circuit to an invariant set which consists of its nontrivial equilibria. Moreover, we show for the first time that the closed loop modified Chua's circuit satisfies set stability which can be considered as a generalization of common Lyapunov stability of an equilibrium point. Simulation results are presented to verify our method.

STRANGE ATTRACTORS IN PERIODICALLY KICKED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (01) ◽  
pp. 83-98 ◽  
Author(s):  
QIUDONG WANG ◽  
ALI OKSASOGLU
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Strange Attractors ◽  
External Forcing ◽  
Chua’S Circuit ◽  
New Developments ◽  
Chua's Circuit

In this paper, we discuss a new mechanism for chaos in light of some new developments in the theory of dynamical systems. It was shown in [Wang & Young, 2002b] that strange attractors occur when an autonomous system undergoing a generic Hopf bifurcation is subjected to a weak external forcing that is periodically turned on and off. For illustration purposes, we apply these results to the Chua's system. Derivation of conditions for chaos along with the results of numerical simulations are presented.

scholarly journals CANARDS FROM CHUA'S CIRCUIT

2013 ◽  
Vol 23 (04) ◽  
pp. 1330010 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
JAUME LLIBRE ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Singularly Perturbed ◽  
Fast Variable ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Flow Curvature ◽  
Cubic Model ◽  
Generic Existence

The aim of this work is to extend Benoît's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.

THE THEORY OF CONFINORS IN CHUA’S CIRCUIT: ACCURATE ANALYSIS OF BIFURCATIONS AND ATTRACTORS

1993 ◽  
Vol 03 (02) ◽  
pp. 333-361 ◽  
Author(s):  
RENÉ LOZI ◽  
SHIGEHIRO USHIKI
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Phase Portrait ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Bifurcation Diagrams ◽  
Accurate Analysis ◽  
Chua's Circuit

We apply the new concept of confinors and anti-confinors, initially defined for ordinary differential equations constrained on a cusp manifold, to the equations governing the circuit dynamics of Chua’s circuit. We especially emphasize some properties of the confinors of Chua’s equation with respect to the patterns in the time waveforms. Some of these properties lead to a very accurate numerical method for the computation of the half-Poincaré maps which reveal the precise structures of Chua’s strange attractors and the exact bifurcation diagrams with the help of a special sequence of change of coordinates. We also recall how such accurate methods allow the reliable numerical observation of the coexistence of three distinct chaotic attractors for at least one choice of the parameters. Chua’s equation seemssurprisingly rich in very new behaviors not yet reported even in other dynamical systems. The application of the theory of confinors to Chua’s equation and the use of sequences of Taylor’s coordinates could give new perspectives to the study of dynamical systems by uncovering very unusual behaviors not yet reported in the literature. The main paradox here is that the theory of confinors, which could appear as a theory of rough analysis of the phase portrait of Chua’s equation, leads instead to a very accurate analysis of this phase portrait.

New Discontinuity-Induced Bifurcations in Chua's Circuit

2015 ◽  
Vol 25 (06) ◽  
pp. 1550090 ◽  
Author(s):  
Shihui Fu ◽  
Qishao Lu ◽  
Xiangying Meng
Keyword(s):  
Dynamical Systems ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chua’S Circuit ◽  
Jacobian Matrices ◽  
Chua's Circuit ◽  
Before And After ◽  
Boundary Equilibrium ◽  
Discontinuous Bifurcations ◽  
Nonsmooth Dynamical Systems

Chua's circuit, an archetypal example of nonsmooth dynamical systems, exhibits mostly discontinuous bifurcations. More complex dynamical phenomena of Chua's circuit are presented here due to discontinuity-induced bifurcations. Some new kinds of classical bifurcations are revealed and analyzed, including the coexistence of two classical bifurcations and bifurcations of equilibrium manifolds. The local dynamical behavior of the boundary equilibrium points located on switch boundaries is found to be determined jointly by the Jacobian matrices evaluated before and after switching. Some new discontinuous bifurcations are also observed, such as the coexistence of two discontinuous and one classical bifurcation.

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