scholarly journals Simultaneous Amplitude and Frequency Noise Analysis in Chua's Circuit

2003 ◽  
Vol 13 (08) ◽  
pp. 2301-2308
Author(s):  
J.-M. Friedt ◽  
D. Gillet ◽  
M. Planat
Keyword(s):  
Noise Analysis ◽  
Frequency Noise ◽  
Bifurcation Parameter ◽  
Chua’S Circuit ◽  
Allan Deviation ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Colpitts Oscillator ◽  
Chua's Circuit ◽  
Amplitude Data

A large number of simultaneous frequency and amplitude data from an electronic chaotic circuit (Chua's circuit) have been obtained. These acquisitions are validated by plotting the bifurcation diagrams of the experimental data versus the bifurcation parameter. We introduce a topological parallel between the Colpitts oscillator and Chua's circuit, and look for similar behavior of the frequency fluctuations using the Allan deviation.

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.

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.

scholarly journals ESTIMATING PROBABILITY DENSITY FUNCTIONS AND ENTROPIES OF CHUA'S CIRCUIT USING B-SPLINE FUNCTIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250107 ◽  
Author(s):  
F. A. SAVACI ◽  
M. GÜNGÖR
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
The State ◽  
Spline Functions ◽  
Density Estimator ◽  
Density Functions ◽  
Bifurcation Parameter ◽  
Chua’S Circuit ◽  
B Spline ◽  
Chua's Circuit

In this paper, first the probability density functions (PDFs) of the states of Chua's circuit have been estimated using B-spline functions and then the state entropies of Chua's circuit with respect to the bifurcation parameter have been obtained. The results of the proposed B-spline density estimator have been compared with the results obtained from the Parzen density estimator.

Realization of Chaotic Circuits Using Lambda Diode

2017 ◽  
Vol 26 (12) ◽  
pp. 1750189 ◽  
Author(s):  
Bibha Kumari ◽  
Nisha Gupta
Keyword(s):  
Chaotic Behavior ◽  
Negative Resistance ◽  
Chaotic Oscillator ◽  
Chua’S Circuit ◽  
Linear Element ◽  
Chaotic Circuit ◽  
Poincaré Plot ◽  
Chua's Circuit ◽  
Nonlinear Resistor ◽  
Wide Range

This paper presents the design of novel autonomous and non-autonomous inductorless chaotic circuit using lambda diode. The autonomous chaotic circuit is implemented using Chua’s circuit, where the piece-wise linear element of Chua’s circuit called Chua’s diode is replaced by lambda diode. The lambda diode used as a nonlinear resistor in Chua’s circuit comprises of BJT, FET and resistors. The non-autonomous chaotic circuit is studied by replacing the piece-wise linear element of Murali–Lakshmana–Chua (MLC) circuit by lambda diode. The reason for employing lambda diode is that it has a wide range of negative resistance characteristics, which enable the circuit to operate at higher frequency ranges. The resulting chaotic oscillator can easily be made to operate at both low and high frequencies. The chaotic behavior of the circuit is established through Multisim simulations in the time and frequency domains. Both theoretical analysis and electronic circuit experiments are presented. The circuit’s chaotic characteristics are further confirmed by means of Poincare plot and the Bifurcation diagram. The observed route to chaos is period-adding.

SOFTENING THE NONLINEARITY IN CHUA'S CIRCUIT

1996 ◽  
Vol 06 (01) ◽  
pp. 179-183 ◽  
Author(s):  
J. M. LIPTON ◽  
K. P. DABKE
Keyword(s):  
Frequency Domain ◽  
High Frequency ◽  
Frequency Noise ◽  
Chua’S Circuit ◽  
High Frequency Noise ◽  
Chua's Circuit ◽  
Low Pass

The effects of both hard and soft nonlinearities are examined in the frequency domain. Softening the hard nonlinearity in Chua's diode has a similar effect to low pass filtering or reducing the level of high frequency noise components.

DYNAMICS OF THE NONAUTONOMOUS CHUA'S CIRCUIT

1995 ◽  
Vol 05 (06) ◽  
pp. 1525-1540 ◽  
Author(s):  
V. C. ANISHCHENKO ◽  
T. E. VADIVASOVA ◽  
D. E. POSTNOV ◽  
O. V. SOSNOVTSEVA ◽  
C. W. WU ◽  
...  
Keyword(s):  
Computer Simulations ◽  
External Forcing ◽  
Chua’S Circuit ◽  
Control Parameters ◽  
Bifurcation Diagrams ◽  
Chua's Circuit ◽  
Physical Experiments ◽  
Additional Control ◽  
Dynamical Regimes ◽  
Two Parameters

In this paper, we investigate via physical experiments and computer simulations the response of Chua's circuit under periodic external forcing. The amplitude and frequency of the external forcing form two additional control parameters, and we present bifurcation diagrams on the plane of these two parameters. We investigate the behavior of Chua's circuit due to external forcing when the unforced circuit is in various dynamical regimes. We finally compare our results with those obtained from a nonautonomous oscillator with an inertial nonlinearity.

ANYONE CAN BUILD CHUA'S CIRCUIT: HANDS-ON-EXPERIENCE WITH CHAOS THEORY FOR HIGH SCHOOL STUDENTS

2009 ◽  
Vol 19 (04) ◽  
pp. 1113-1125 ◽  
Author(s):  
GAURAV GANDHI ◽  
GYÖRGY CSEREY ◽  
JOHN ZBROZEK ◽  
TAMÁS ROSKA
Keyword(s):  
High School Students ◽  
Chaos Theory ◽  
Electronic Circuit ◽  
Chua’S Circuit ◽  
Chaotic Circuit ◽  
School Students ◽  
Computer Screen ◽  
Chua's Circuit ◽  
Hands On ◽  
Electronic Implementation

Chaos is a physical and mathematical phenomenon discovered by E. Lorenz in 1963. The first simple electronic implementation had been invented by L. O. Chua in 1984. This electronic circuit, called Chua's circuit was designed for ease of implementation. In the current brief we will explain chaos by building Chua's chaotic circuit using our Chua's circuit kit with inexpensive components. For readers without access to an oscilloscope, this paper proposes the use of a laptop/Personal Computer to capture the voltage waveforms generated from the circuit and plot the waveforms on a computer screen using a virtual oscilloscope software provided by the authors. The kit is available, the software is downloadable.

A MODIFIED CHUA'S CIRCUIT WITH AN ATTRACTION-REPULSION FUNCTION

2008 ◽  
Vol 18 (07) ◽  
pp. 1865-1888 ◽  
Author(s):  
RONG LI ◽  
ZHISHENG DUAN ◽  
BO WANG ◽  
GUANRONG CHEN
Keyword(s):  
Computer Simulations ◽  
Piecewise Linear ◽  
Nonlinear Function ◽  
Piecewise Linear Function ◽  
Stability Conditions ◽  
Chua’S Circuit ◽  
Bifurcation Diagrams ◽  
Chua's Circuit ◽  
Dynamical Behaviors ◽  
New System

In this paper, the original Chua's circuit is modified by substituting its piecewise-linear function with an attraction-repulsion function. Some new complex dynamical behaviors such as chaos are observed through computer simulations. Basic properties of the new circuit are analyzed by means of bifurcation diagrams. Lagrange stability conditions of the circuit are derived. A comparison between this modified Chua's circuit with an attraction-repulsion function and the modified Chua's circuit with a cubic nonlinear function is presented. Moreover, a generalization of the new circuit that can generate multiple scrolls is designed and simulated. Finally, a physical circuit is built to visualize the new system, with some experimental observations reported.

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