Computation of supertrack functions for Chua’s oscillator and for Chua’s circuit with memristor

2021 ◽  
Vol 94 ◽  
pp. 105568
Author(s):  
Fabio Caldarola ◽  
Pietro Pantano ◽  
Eleonora Bilotta
Keyword(s):  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Chua’S Oscillator

CHARACTERISATION OF CHAOS IN CHUA'S OSCILLATOR IN TERMS OF UNSTABLE PERIODIC ORBITS

1993 ◽  
Vol 03 (02) ◽  
pp. 411-429 ◽  
Author(s):  
MACIEJ J. OGORZAŁEK ◽  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Picture Book ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Canonical Chua’S Circuit

We present a picture book of unstable periodic orbits embedded in typical chaotic attractors found in the canonical Chua's circuit. These include spiral Chua's, double-scroll Chua's and double hook attractors. The "skeleton" of unstable periodic orbits is specific for the considered attractor and provides an invariant characterisation of its geometry.

scholarly journals NUMERICAL INVESTIGATION OF SIGNAL AMPLIFICATION VIA VIBRATIONAL RESONANCE IN CHUA'S CIRCUIT

2020 ◽  
Vol 6 ◽  
pp. 14
Author(s):  
John Abidemi Laoye ◽  
Taiwo Olakunle Roy-Layinde ◽  
Kehinde Adam Omoteso ◽  
Rasaki Kola Odunaike
Keyword(s):  
Low Frequency ◽  
Response Amplitude ◽  
Chua’S Circuit ◽  
Response Curves ◽  
Vibrational Resonance ◽  
Periodic Force ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Conductance Parameter ◽  
Cubic Polynomial

In this paper, we numerically investigated the occurrence of Vibrational Resonance in a modified Chua's oscillator with a smooth nonlinearity, described by a cubic polynomial. Response curves generated from the numerical simulation at the low frequency reveal that the system's response amplitude could be controlled by modulating the conductance parameter of the Chua's circuit, rather modulating the parameters of the fast-periodic force. Modulating the frequency of the fast-periodic force slightly reduces the response amplitude; shifts the peak point to a higher value of the amplitude of the fast-periodic force by widening the resonance curves. Within certain parameter regime of the high frequency (Ω >100ω), the system's response gets saturated, and further increase does not affect its amplitude.

CHUA'S OSCILLATOR: A ZOO OF ATTRACTORS

1993 ◽  
Vol 03 (02) ◽  
pp. 309-359 ◽  
Author(s):  
PHILIPPE DEREGEL
Keyword(s):  
Vector Fields ◽  
Piecewise Linear ◽  
Topological Equivalence ◽  
Chua’S Circuit ◽  
Explicit Formulas ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
In Series ◽  
User Friendly ◽  
Circuit Family

Chaos has been widely reported and studied in Chua's circuit family, which is characterized by a 21 parameter family of odd-symmetric piecewise-linear vector fields in R3. In this tutorial paper, we shall prove that, up to a topological equivalence, all the dynamics of this family are subsumed within that of a single circuit: Chua's oscillator; directly derived from Chua's circuit by adding a resistor in series with the inductor. We provide explicit formulas of the parameters of Chua's oscillator leading to a behavior qualitatively identical to that of any system belonging to Chua's circuit family. These formulas are then used to construct, in an almost trivial way, a gallery of (quasiperiodic and strange) attractors belonging to Chua's circuit family. A user-friendly program is available to allow a better understanding of the evolution of the dynamics as a function of the parameters of Chua's oscillator, and to follow the trajectory in the eigenspaces.

ON THE APPROXIMATE ONE-D MAP IN CHUA'S OSCILLATOR

2005 ◽  
Vol 15 (08) ◽  
pp. 2545-2550 ◽  
Author(s):  
PEADAR FORBES ◽  
SARAH BOYLE ◽  
KEITH O'DONOGHUE ◽  
MICHAEL PETER KENNEDY
Keyword(s):  
Piecewise Linear ◽  
Initial Slope ◽  
Chua’S Circuit ◽  
Linear Dynamics ◽  
One Dimensional ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Strong Contraction ◽  
Simulation And Experiment

Due to strong contraction in the outer regions of Chua's circuit with piecewise-linear dynamics, the system can be described by an approximate one-dimensional map. We confirm by simulation and experiment that the initial slope of this map is defined by [Formula: see text].

DISCRETE CHAOTIC DYNAMICS FROM CHUA'S OSCILLATOR: CHUA MACHINES

2009 ◽  
Vol 19 (01) ◽  
pp. 1-115 ◽  
Author(s):  
ELEONORA BILOTTA ◽  
PIETRO PANTANO
Keyword(s):  
Parameter Space ◽  
Iterative Process ◽  
Chaotic Dynamics ◽  
Formal Description ◽  
Chua’S Circuit ◽  
Computational System ◽  
3D Images ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Qualitative Changes

In previous work, the authors explored the parameter space for Chua's circuit and its generalizations, discovering new routes to chaos, and nearly a thousand new attractors. These were obtained by varying the parameters of the physical circuit and of systems derived from it. Here, we present a novel class of computational system that does not respect the classical constraints in Chua's circuit, and that generates chaotic dynamics via an iterative process based on discrete versions of the equations for Chua's circuit and its variants. We call these systems Chua Machines. After presenting the chaotic dynamics, we provide a formal description of Chua Machines and a Gallery of 222 3D images, illustrating their dynamics. We discuss the method used to discover these systems and the metrics applied in the exploration of their parameter space and offer examples of highly complex bifurcation maps, together with images showing how patterns can evolve with time, or vary significantly changing the values of one of the parameters. Finally, we present a detailed analysis of qualitative changes in a Chua Machine as it traverses the parameter space of the bifurcation map. The evidence suggests that these dynamics are even richer and more complex than their counterpart in the continuous domain.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

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