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.

scholarly journals EXPERIMENTAL EVIDENCE FOR VIBRATIONAL RESONANCE AND ENHANCED SIGNAL TRANSMISSION IN CHUA'S CIRCUIT

2013 ◽  
Vol 23 (11) ◽  
pp. 1350189 ◽  
Author(s):  
R. JOTHIMURUGAN ◽  
K. THAMILMARAN ◽  
S. RAJASEKAR ◽  
M. A. F. SANJUÁN
Keyword(s):  
Experimental Evidence ◽  
Low Frequency ◽  
Signal Propagation ◽  
Chua’S Circuit ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Chua's Circuit ◽  
Wide Range

We consider a single Chua's circuit and a system of a unidirectionally coupled n-Chua's circuits driven by a biharmonic signal with two widely different frequencies ω and Ω, where Ω ≫ ω. We show experimental evidence for vibrational resonance in the single Chua's circuit and undamped signal propagation of a low-frequency signal in the system of n-coupled Chua's circuits where only the first circuit is driven by the biharmonic signal. In the single circuit, we illustrate the mechanism of vibrational resonance and the influence of the biharmonic signal parameters on the resonance. In the n(=75)-coupled Chua's circuits enhanced propagation of low-frequency signal is found to occur for a wide range of values of the amplitude of the high-frequency input signal and coupling parameter. The response amplitude of the ith circuit increases with i and attains a saturation. Moreover, the unidirectional coupling is found to act as a low-pass filter.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

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.

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].

ON PERIODIC ORBITS AND HOMOCLINIC BIFURCATIONS IN CHUA’S CIRCUIT WITH A SMOOTH NONLINEARITY

1993 ◽  
Vol 03 (02) ◽  
pp. 363-384 ◽  
Author(s):  
ALEXANDER I. KHIBNIK ◽  
DIRK ROOSE ◽  
LEON O. CHUA
Keyword(s):  
Periodic Orbits ◽  
Bifurcation Theory ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Homoclinic Bifurcation ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Homoclinic Bifurcations ◽  
Cubic Polynomial

We present the bifurcation analysis of Chua’s circuit equations with a smooth nonlinearity, described by a cubic polynomial. Our study focuses on phenomena that can be observed directly in the numerical simulation of the model, and on phenomena which are revealed by a more elaborate analysis based on continuation techniques and bifurcation theory. We emphasize how a combination of these approaches actually works in practice. We compare the dynamics of Chua’s circuit equations with piecewise-linear and with smooth nonlinearity. The dynamics of these two variants are similar, but we also present some differences. We conjecture that this similarity is due to the central role of homoclinicity in this model. We describe different ways in which the type of a homoclinic bifurcation influences the behavior of branches of periodic orbits. We present an overview of codimension 1 bifurcation diagrams for principal periodic orbits near homoclinicity for three-dimensional systems, both in the generic case and in the case of odd symmetry. Most of these diagrams actually occurs in the model. We found several homoclinic bifurcations of codimension 2, related to the so called resonant conditions. We study one of these bifurcations, a double neutral saddle loop.

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.

scholarly journals Effect of Modulated Signals on Vibrational Resonance in a Harmonically Trapped Potential System

2021 ◽  
Vol 13 (3) ◽  
pp. 797-807
Author(s):  
B. Bhuvaneshwari ◽  
S. V. Priyatharsini ◽  
V. Chinnathambi ◽  
S. Rajasekar
Keyword(s):  
Low Frequency ◽  
Response Amplitude ◽  
External Signal ◽  
Amplitude Curve ◽  
Vibrational Resonance ◽  
Potential Wells ◽  
Fm Signals ◽  
Potential System ◽  
Single Well ◽  
Modulated Signals

We consider a harmonically trapped potential system driven by modulated signals with two widely different frequencies ω and Ω, where Ω >> ω. The forms of modulated signals are amplitude modulated (AM) and frequency-modulated (FM) signals. An amplitude-modulated external signal is consisting of a low-frequency (ω) component and two high-frequencies (Ω + ω) and (Ω − ω) whereas the frequency modulated signal consisting of the frequency components such as f sinωt cos(g cosΩt) and f sin(g cosΩt) cosωt. Depending upon the values of the parameters in the potential function, an odd number of potential wells of different depths can be generated. We numerically investigate the effect of these modulated signals on vibrational resonance (VR) in single-well, three-well, five-well and seven-well potentials. Different from traditional VR theory in the present paper, the enhancement of VR is made by the amplitudes of the AM and FM signals. We show the enhanced response amplitude (Q) at the low-frequency ω, showing the greater number of resonance peaks and non-decay response amplitude on the response amplitude curve due to the modulated signals in all the potential wells. Furthermore, the response amplitude of the system driven by the AM signal exhibits hysteresis and a jump phenomenon. Such behavior of Q is not observed in the system driven by the FM signal.

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