CHAOTIC BEATS IN A MODIFIED CHUA'S CIRCUIT: DYNAMIC BEHAVIOR AND CIRCUIT DESIGN

2004 ◽  
Vol 14 (09) ◽  
pp. 3045-3064 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
State Space ◽  
Dynamic Behavior ◽  
Circuit Design ◽  
Time Domain ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Chaotic Beats ◽  
Chaotic Nature

This paper illustrates the recent phenomenon of chaotic beats in a modified version of Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In order to satisfy the constraints imposed by the beats dynamics, a novel implementation of the voltage-controlled characteristic of the Chua diode is proposed. By using Pspice simulator, the behavior of the designed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the approach.

The analysis of chaotic regimes in Chua’s circuit with smooth nonlinearity based on the matrix decomposition method

2019 ◽  
Vol 63 (4) ◽  
pp. 501-512
Author(s):  
A. M. Krot ◽  
U. A. Sychou
Keyword(s):  
Simulation Model ◽  
State Space ◽  
Decomposition Method ◽  
Matrix Decomposition ◽  
Chaotic Regime ◽  
Chua’S Circuit ◽  
Electric Circuits ◽  
Chua's Circuit ◽  
The Matrix ◽  
Matrix Series

The scope of this work are electric circuits or electronic devices with chaotic regimes, in particular the Chua’s circuit. A nonlinear analysis of chaotic attractors based on the Krot’s method of matrix decomposition of vector functions in state-space of complex systems has been used to investigate the Chua’s circuit with smooth nonlinearity. It includes an analysis of linear term of the matrix series as well as an estimation of influence of high order terms of this series on stability of complex system under investigation. Here the method of matrix decomposition has been applied to analysis of the Chua’s attractor. The terms of matrix series have been used to create a simulation model and to reconstruct an attractor of chaotic modes. The proposed simulation model makes it possible to separate an influence of nonlinearities on forming a chaotic regime of the Chua’s circuit. Usage of both the matrix decomposition method and computational experiment has allowed us to find out that the initial turbulence model proposed by L. D. Landau is suitable for set-up description of the chaotic regime of the Chua’s circuit. It is shown that a mode of hard self-excitation in the Chua’s circuit leads to its chaotic regime operating with a double-scroll attractor in the state-space. The results might be used to generate of chaotic oscillations or data encryption. 

Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

2016 ◽  
Vol 26 (10) ◽  
pp. 1630027 ◽  
Author(s):  
M. Paul Asir ◽  
A. Jeevarekha ◽  
P. Philominathan
Keyword(s):  
Phase Space ◽  
Experimental Observation ◽  
Time Domain ◽  
Hardware Implementation ◽  
Nonlinear Element ◽  
State Variables ◽  
Chaotic Beats ◽  
Chaotic Nature ◽  
First Time

This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.

CONTROL OF CHUA'S CIRCUIT

1993 ◽  
Vol 03 (01) ◽  
pp. 173-194 ◽  
Author(s):  
TOM T. HARTLEY ◽  
FARAMARZ MOSSAYEBI
Keyword(s):  
Control Theory ◽  
State Space ◽  
Chaotic System ◽  
Harmonic Balance ◽  
Period Doubling ◽  
Chua’S Circuit ◽  
Input Output ◽  
Chua's Circuit ◽  
Control Approach ◽  
Balance Approach

This paper considers the control of a polynomial variant of the original Chua's circuit. Both state space techniques and input-output techniques are presented. It is shown that standard control theory approaches can easily accommodate a chaotic system. Furthermore, it is shown that a harmonic balance approach could predict the period doubling phenomenon and onset of the double scroll chaos, as well as providing a control approach.

FRACTIONAL-ORDER CHUA'S CIRCUIT: TIME-DOMAIN ANALYSIS, BIFURCATION, CHAOTIC BEHAVIOR AND TEST FOR CHAOS

2008 ◽  
Vol 18 (03) ◽  
pp. 615-639 ◽  
Author(s):  
DONATO CAFAGNA ◽  
GIUSEPPE GRASSI
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Decomposition Method ◽  
Chaotic Behavior ◽  
Adomian Decomposition Method ◽  
Time Domain Analysis ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Adomian Decomposition

In this tutorial the chaotic behavior of the fractional-order Chua's circuit is investigated from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which enables the solution of the fractional differential equations to be found in closed form. By exploiting the capabilities offered by the decomposition method, the paper presents two remarkable findings. The first result is that a novel bifurcation parameter is identified, that is, the fractional-order q of the derivative. The second result is that chaos exists in the fractional Chua's circuit with order q = 1.05, which is the lowest order reported in literature for such circuits. Finally, a reliable and efficient binary test for chaos (called "0–1 test") is utilized to detect the presence of chaotic attractors in the system dynamics.

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.

scholarly journals A novel approach for Chua’s circuit design and its hardware implementation

2006 ◽  
Vol 55 (8) ◽  
pp. 3938
Author(s):  
Li Ya ◽  
Yu Si-Min ◽  
Dai Qing-Yun ◽  
Liu Ming-Hua ◽  
Liu Qing
Keyword(s):  
Circuit Design ◽  
Hardware Implementation ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Novel Approach

scholarly journals Fractional-Order Analysis of Modified Chua’s Circuit System with the Smooth Degree of 3 and Its Microcontroller-Based Implementation with Analog Circuit Design

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 340
Author(s):  
Junxia Wang ◽  
Li Xiao ◽  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Serdar Cicek ◽  
...  
Keyword(s):  
Circuit Design ◽  
Fractional Order ◽  
Analog Circuit ◽  
Continuous System ◽  
Order System ◽  
Chua’S Circuit ◽  
Coexisting Attractors ◽  
Chua's Circuit ◽  
Order Analysis ◽  
Digital Engineering

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system.

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