STOCHASTIC RESONANCE IN CHUA’S CIRCUIT

1992 ◽  
Vol 02 (02) ◽  
pp. 397-401 ◽  
Author(s):  
V.S. ANISHCHENKO ◽  
M.A. SAFONOVA ◽  
L.O. CHUA
Keyword(s):  
Stochastic Resonance ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Physical Mechanism ◽  
Sinusoidal Signal ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
System Parameters ◽  
Coherent Interaction ◽  
Chaotic Electronic Circuit

In this paper, we report numerical observations of the stochastic resonance (SR) phenomenon in a bistable chaotic electronic circuit (namely, Chua’s circuit) driven simultaneously by noise and a sinusoidal signal. It is shown that the noise-induced “chaos-chaos” type intermittency is a physical mechanism of the SR-phenomenon in chaotic systems. The resulting amplification of the sinusoidal signal intensity is due to a coherent interaction of three characteristic frequencies of the system. The SR-phenomenon can be controlled by a variation of either the noise intensity or the system parameters in the absence of noise.

STOCHASTIC RESONANCE IN THE NONAUTONOMOUS CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 553-578 ◽  
Author(s):  
V. S. ANISHCHENKO ◽  
M. A. SAFONOVA ◽  
L. O. CHUA
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Modulation Frequency ◽  
External Noise ◽  
Statistical Characteristics ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Coherent Interaction ◽  
Parameter Variations ◽  
Dynamics Method

The dynamics of the nonautonomous Chua's circuit driven by a sinusoidal signal and additive noise is investigated numerically via the "two-state" dynamics method. The possibility of realizing the phenomenon of stochastic resonance (SR) is established. The SR is characterized by an increase in the signal-to-noise ratio (SNR) due to the coherent interaction between the characteristic frequencies of the chaotic bistable Chua's circuit and the modulation frequency of the input. The SNR can be controlled by both external noise and system parameter variations in this circuit. The statistical characteristics of the "chaos-chaos" type intermittency and their correlation with the optimal conditions for SR are investigated.

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.

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.

STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS

1994 ◽  
Vol 04 (02) ◽  
pp. 441-446 ◽  
Author(s):  
V.S. ANISHCHENKO ◽  
M.A. SAFONOVA ◽  
L.O. CHUA
Keyword(s):  
Numerical Simulation ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Signal Distortion ◽  
Signal To Noise ◽  
Chua's Circuit ◽  
Noise Ratio ◽  
Modulated Signals

Using numerical simulation, we establish the possibility of realizing the stochastic resonance (SR) phenomenon in Chua’s circuit when it is excited by either an amplitude-modulated or a frequency-modulated signal. It is shown that the application of a frequency-modulated signal to a Chua’s circuit operating in a regime of dynamical intermittency is preferable over an amplitude-modulated signal from the point of view of minimizing the signal distortion and maximizing the signal-to-noise ratio (SNR).

Stochastic Multiresonance in an Electronic Chaotic Circuit

2014 ◽  
Vol 24 (03) ◽  
pp. 1450027
Author(s):  
Thomas Stemler ◽  
Johannes P. Werner ◽  
Hartmut Benner
Keyword(s):  
Stochastic Resonance ◽  
Linear Response ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Stochastic Systems ◽  
Electronic Circuit ◽  
Chaotic Circuit ◽  
Applied Method

Methods to estimate the amplification by stochastic resonance are tested in an electronic circuit experiment showing chaotic dynamics. We demonstrate that the linear response ansatz used for the estimation in stochastic systems can be also applied to chaotic systems showing crisis induced intermittency. In addition, the applied method explains the mechanism leading to stochastic multiresonance.

Experimental study of stochastic resonance in a Chua’s circuit operating in a chaotic regime

2006 ◽  
Vol 219 (1) ◽  
pp. 93-100 ◽  
Author(s):  
Wojciech Korneta ◽  
Iacyel Gomes ◽  
Claudio R. Mirasso ◽  
Raúl Toral
Keyword(s):  
Experimental Study ◽  
Stochastic Resonance ◽  
Chaotic Regime ◽  
Chua’S Circuit ◽  
Chua's Circuit

THEORY AND EXPERIMENT OF A FIRST-ORDER CHAOTIC DELAY DYNAMICAL SYSTEM

2013 ◽  
Vol 23 (06) ◽  
pp. 1330020 ◽  
Author(s):  
TANMOY BANERJEE ◽  
DEBABRATA BISWAS
Keyword(s):  
Time Delay ◽  
Electronic Circuit ◽  
Stable Limit Cycle ◽  
Nonlinear Behavior ◽  
Mathematical Function ◽  
Hyperchaotic System ◽  
Stable Limit ◽  
System Parameters ◽  
Chaotic Electronic Circuit ◽  
Theory And Experiment

We report the theory and experiment of a new time-delayed chaotic (hyperchaotic) system with a single scalar time delay and a nonlinearity described by a closed form mathematical function. Detailed stability and bifurcation analyses establish that with the suitable delay and system parameters, the system shows a stable limit cycle through a supercritical Hopf bifurcation. Numerical simulations exemplify that the system depicts mono-scroll and double-scroll chaos and hyperchaos for a range of delay and other system parameters. Nonlinear behavior of the system is characterized by Lyapunov exponents and Kaplan–Yorke dimension. It is established that, for some suitably chosen system parameters, the system shows hyperchaos even for a small or moderate time delay. Finally, the system is implemented in an analogue electronic circuit using off-the-shelf circuit elements. It is shown that the behavior of the time delay chaotic electronic circuit qualitatively agrees well with our analytical and numerical results.

Detecting Weak Signals by Using Memristor-Involved Chua’s Circuit and Verification in Experimental Platform

2020 ◽  
Vol 30 (13) ◽  
pp. 2050193
Author(s):  
Li Xiong ◽  
Xinguo Zhang ◽  
Sufen Teng ◽  
Liwan Qi ◽  
Peijin Zhang
Keyword(s):  
Comparative Research ◽  
Chaotic Systems ◽  
Short Circuit ◽  
Characteristic Curve ◽  
Detection Methods ◽  
Measurement Unit ◽  
Chua’S Circuit ◽  
Weak Signals ◽  
Chua's Circuit ◽  
Research Platform

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.

Synchronization through Compound Chaotic Signal in Chua's Circuit and Murali–Lakshmanan–Chua Circuit

1997 ◽  
Vol 07 (02) ◽  
pp. 415-421 ◽  
Author(s):  
K. Murali ◽  
M. Lakshmanan
Keyword(s):  
Feedback Loop ◽  
Chaotic Systems ◽  
Chaotic Signal ◽  
Drive System ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Response System ◽  
Chua Circuit ◽  
Response Systems ◽  
System Variables

In this letter the idea of synchronization of chaotic systems is further extended to the case where all the drive system variables are combined to obtain a compound chaotic drive signal. An appropriate feedback loop is constructed in the response system to achieve synchronization among the variables of drive and response systems. We apply this method of synchronization to the familiar Chua's circuit and Murali–Lakshmanan–Chua circuit equations.

CONTROLLING CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 139-149 ◽  
Author(s):  
GUANRONG CHEN ◽  
XIAONING DONG
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Control Process ◽  
Periodic Signal ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Simulation Results ◽  
Feedback Control Strategy

The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the well-known Chua's circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. Simple sufficient conditions for the controllability of this particular circuit are established. Simulation results are included to visualize the control process. A circuit implementation of the designed feedback control is realized by adding a linear resistor and an appropriate periodic-signal generator to the original circuit.

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