scholarly journals OBSERVATION OF CHAOTIC BEATS IN A DRIVEN MEMRISTIVE CHUA'S CIRCUIT

2011 ◽  
Vol 21 (03) ◽  
pp. 737-757 ◽  
Author(s):  
A. ISHAQ AHAMED ◽  
K. SRINIVASAN ◽  
K. MURALI ◽  
M. LAKSHMANAN
Keyword(s):  
Numerical Simulations ◽  
External Force ◽  
Piecewise Linear ◽  
Statistical Analyses ◽  
Suitable Choice ◽  
Time Varying ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Chaotic Beats ◽  
External Driving

In this paper, a time varying resistive circuit realizing the action of an active three segment piecewise linear flux controlled memristor is proposed. Using this as the nonlinearity, a driven Chua's circuit is implemented. The phenomenon of chaotic beats in this circuit is observed for a suitable choice of parameters. The memristor acts as a chaotically time varying resistor (CTVR), switching between a less conductive OFF state and a more conductive ON state. This chaotic switching is governed by the dynamics of the driven Chua's circuit of which the memristor is an integral part. The occurrence of beats is essentially due to the interaction of the memristor aided self-oscillations of the circuit and the external driving sinusoidal forcing. Upon slight tuning/detuning of the frequencies of the memristor switching and that of the external force, constructive and destructive interferences occur leading to revivals and collapses in amplitudes of the circuit variables, which we refer as chaotic beats. Numerical simulations and Multisim modeling as well as statistical analyses have been carried out to observe as well as to understand and verify the mechanism leading to chaotic beats.

CHUA’S CIRCUIT: AN OVERVIEW TEN YEARS LATER

1994 ◽  
Vol 04 (02) ◽  
pp. 117-159 ◽  
Author(s):  
LEON O. CHUA
Keyword(s):  
Secure Communication ◽  
Vector Fields ◽  
Piecewise Linear ◽  
International Workshop ◽  
Noise Spectrum ◽  
Chaotic Regime ◽  
Practical Significance ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
New Phenomena

More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol. 40, no. 10, October, 1993), an International Workshop on Chua’s Circuit: chaotic phenomena and applica tions at NOLTA’93, and a book (edited by R.N. Madan, World Scientific, 1993) on Chua’s circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last six months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua’s circuit. The robustness of this IC chip demonstrates that an array of Chua’s circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua’s circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua’s circuit— now generally referred to as Chua’s oscillator. This circuit is most significant because it is structurally the simplest (it contains only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21-parameter family of continuous odd-symmetric piecewise-linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua’s circuits, e.g., stochastic resonance, chaos-chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua’s circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua’s circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g. secure communication.

CONTROL OF n-SCROLL CHUA'S CIRCUIT

2009 ◽  
Vol 19 (11) ◽  
pp. 3813-3822 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
BILEL SAYOUD ◽  
HAMZA BOUMAIZA ◽  
NOURA MANSOURI
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Predictive Control ◽  
Control Method ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

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.

STABILITY OF OBSERVER-BASED CHAOTIC COMMUNICATIONS FOR A CLASS OF LUR'E SYSTEMS

2002 ◽  
Vol 12 (07) ◽  
pp. 1605-1618 ◽  
Author(s):  
JOSE ALVAREZ-RAMIREZ ◽  
HECTOR PUEBLA ◽  
ILSE CERVANTES
Keyword(s):  
Numerical Simulations ◽  
Chaotic Oscillator ◽  
Chua’S Circuit ◽  
Lur’E Systems ◽  
Chua's Circuit ◽  
Information Signal ◽  
Synchronization Signal ◽  
Chaotic Communications ◽  
The Stability

In this paper, the stability of observer-based chaotic communications using Lur'e systems is presented. In this approach, the transmitter contains a chaotic oscillator with an input that is modulate by the information signal. The receiver is composed by a copy of the transmitter driven by a synchronization signal. Some effects of transmission noise on the demodulation procedure are discussed. Numerical simulations on Chua's circuit are provided to illustrate our findings.

FLUCTUATIONS IN THE STATE OF CHAOS-CHAOS INTERMITTENCY OF CHUA’S CIRCUIT

1995 ◽  
Vol 05 (01) ◽  
pp. 271-273
Author(s):  
M. KOCH ◽  
R. TETZLAFF ◽  
D. WOLF
Keyword(s):  
Power Spectrum ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
The State ◽  
Circuit Parameter ◽  
Chua’S Circuit ◽  
External Excitation ◽  
Chua's Circuit ◽  
Parameter Values

We studied the power spectrum of the normalized voltage across the capacitor parallel to a piecewise-linear resistor of Chua’s circuit in the “chaos-chaos intermittency” state [Anishchenko et al., 1992]. The investigations included various initial conditions and circuit parameter values without and with external excitation. In all cases we found spectra showing a 1/ω2-decay over more than four decades.

MAXIMUM DYNAMIC RANGE OF BIFURCATION OF CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 471-481 ◽  
Author(s):  
A. A. A. NASSER ◽  
E. E. HOSNY ◽  
M. I. SOBHY
Keyword(s):  
Linear Function ◽  
Dynamic Range ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Bifurcation Parameter ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Simulation Results

This paper includes a method for detecting the maximum possible range of bifurcations based upon the multilevel oscillation technique. An application of the method to Chua's circuit, and new simulation results using the slope of the piecewise-linear function as a bifurcation parameter are presented.

DIGITAL SIGNAL PROCESSOR-BASED INVESTIGATION OF CHUA'S CIRCUIT FAMILY

1993 ◽  
Vol 03 (02) ◽  
pp. 269-292 ◽  
Author(s):  
MICHAEL PETER KENNEDY ◽  
CHAI WAH WU ◽  
STANLEY PAU ◽  
JAMES TOW
Keyword(s):  
Digital Signal Processor ◽  
Piecewise Linear ◽  
Digital Signal ◽  
Chua’S Circuit ◽  
Single Chip ◽  
Integration Algorithm ◽  
Chua's Circuit ◽  
Multistep Integration ◽  
Circuit Family ◽  
Signal Processor

This paper is concerned with exploiting the architecture of a single-chip digital signal processor for integrating piecewise-linear ODEs. We show that DSPs can be usefully applied in the study of Chua's circuit family provided that one chooses a multistep integration algorithm which exploits their unique single-instruction multiply-and-accumulate feature.

A NEW LOOK AT CHUA'S CIRCUIT

2011 ◽  
Vol 21 (06) ◽  
pp. 1653-1666 ◽  
Author(s):  
ICHRAF EL GAMMOUDI ◽  
MOEZ FEKI
Keyword(s):  
Numerical Simulations ◽  
Chaotic Behavior ◽  
Experimental Results ◽  
Chua’S Circuit ◽  
Systematic Method ◽  
Chua's Circuit ◽  
New Look

This paper proposes a novel way to look at Chua's circuit and to investigate its chaotic behavior. We propose a systematic method to increase the dimension of Chua's circuit and to choose the element values. Our claims are confirmed by numerical simulations on Chua's circuit and on modified Chua's circuit and also supported by experimental results.

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