scholarly journals NONSMOOTH BIFURCATIONS, TRANSIENT HYPERCHAOS AND HYPERCHAOTIC BEATS IN A MEMRISTIVE MURALI–LAKSHMANAN–CHUA CIRCUIT

2013 ◽  
Vol 23 (06) ◽  
pp. 1350098 ◽  
Author(s):  
A. ISHAQ AHAMED ◽  
M. LAKSHMANAN
Keyword(s):  
Time Series ◽  
Piecewise Linear ◽  
Power Spectra ◽  
Phase Portraits ◽  
Chua Circuit ◽  
Smooth System ◽  
Zero Time ◽  
Active Flux ◽  
Time Discontinuity ◽  
Grazing Bifurcations

In this paper, a memristive Murali–Lakshmanan–Chua (MLC) circuit is built by replacing the nonlinear element of an ordinary MLC circuit, namely the Chua's diode, with a three-segment piecewise-linear active flux controlled memristor. The bistability nature of the memristor introduces two discontinuity boundaries or switching manifolds in the circuit topology. As a result, the circuit becomes a piecewise-smooth system of second order. Grazing bifurcations, which are essentially a form of discontinuity-induced nonsmooth bifurcations, occur at these boundaries and govern the dynamics of the circuit. While the interaction of the memristor-aided self oscillations of the circuit and the external sinusoidal forcing result in the phenomenon of beats occurring in the circuit, grazing bifurcations endow them with chaotic and hyperchaotic nature. In addition, the circuit admits a codimension-5 bifurcation and transient hyperchaos. Grazing bifurcations as well as other behaviors have been analyzed numerically using time series plots, phase portraits, bifurcation diagram, power spectra and Lyapunov spectrum, as well as the recent 0–1 K test for chaos, obtained after constructing a proper Zero Time Discontinuity Map (ZDM) and Poincaré Discontinuity Map (PDM) analytically. Multisim simulations using a model of piecewise linear memristor have also been used to confirm some of the behaviors.

scholarly journals Sliding Bifurcations in the Memristive Murali–Lakshmanan–Chua Circuit and the Memristive Driven Chua Oscillator

2020 ◽  
Vol 30 (14) ◽  
pp. 2050214
Author(s):  
A. Ishaq Ahamed ◽  
M. Lakshmanan
Keyword(s):  
Numerical Simulations ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Filippov Systems ◽  
Chua Circuit ◽  
Linear Characteristic ◽  
Discontinuity Mapping ◽  
Chua Oscillator ◽  
Zero Time ◽  
Time Discontinuity

In this paper, we report the occurrence of sliding bifurcations admitted by the memristive Murali–Lakshmanan–Chua circuit [Ishaq & Lakshmanan, 2013] and the memristive driven Chua oscillator [Ishaq et al., 2011]. Both of these circuits have a flux-controlled active memristor designed by the authors in 2011, as their nonlinear element. The three-segment piecewise-linear characteristic of this memristor bestows on the circuits two discontinuity boundaries, dividing their phase spaces into three subregions. For proper choice of parameters, these circuits take on a degree of smoothness equal to one at each of their two discontinuities, thereby causing them to behave as Filippov systems. Sliding bifurcations, which are characteristic of Filippov systems, arise when the periodic orbits in each of the subregions, interact with the discontinuity boundaries, giving rise to many interesting dynamical phenomena. The numerical simulations are carried out after incorporating proper zero time discontinuity mapping (ZDM) corrections. These are found to agree well with the experimental observations which we report here appropriately.

scholarly journals Discontinuity Induced Hopf and Neimark–Sacker Bifurcations in a Memristive Murali–Lakshmanan–Chua Circuit

2017 ◽  
Vol 27 (06) ◽  
pp. 1730021 ◽  
Author(s):  
A. Ishaq Ahamed ◽  
M. Lakshmanan
Keyword(s):  
Floquet Theory ◽  
Equilibrium Points ◽  
Multiple Equilibrium ◽  
Hopf Bifurcations ◽  
Chua Circuit ◽  
Local Bifurcations ◽  
Generalized Differential ◽  
Multiple Equilibrium Points ◽  
Zero Time ◽  
Time Discontinuity

We report using Clarke’s concept of generalized differential and a modification of Floquet theory to nonsmooth oscillations, the occurrence of discontinuity induced Hopf bifurcations and Neimark–Sacker bifurcations leading to quasiperiodic attractors in a memristive Murali–Lakshmanan–Chua (memristive MLC) circuit. The above bifurcations arise because of the fact that a memristive MLC circuit is basically a nonsmooth system by virtue of having a memristive element as its nonlinearity. The switching and modulating properties of the memristor which we have considered endow the circuit with two discontinuity boundaries and multiple equilibrium points as well. As the Jacobian matrices about these equilibrium points are noninvertible, they are nonhyperbolic, some of these admit local bifurcations as well. Consequently when these equilibrium points are perturbed, they lose their stability giving rise to quasiperiodic orbits. The numerical simulations carried out by incorporating proper discontinuity mappings (DMs), such as the Poincaré discontinuity map (PDM) and zero time discontinuity map (ZDM), are found to agree well with experimental observations.

Dynamics of SC-CNN Based Variant of MLC Circuit: An Experimental Study

2014 ◽  
Vol 24 (02) ◽  
pp. 1430008 ◽  
Author(s):  
P. S. Swathy ◽  
K. Thamilmaran
Keyword(s):  
Neural Network ◽  
Experimental Study ◽  
Time Series ◽  
Power Spectra ◽  
Cellular Neural Network ◽  
Phase Portraits ◽  
Onset Of Chaos ◽  
Experimental Time Series ◽  
The Stability ◽  
Good Agreement

In this paper, a State Controlled Cellular Neural Network (SC-CNN) based variant of Murali–Lakshmanan–Chua (MLCV) circuit is presented. The proposed system is modeled by using a suitable connection of two simple state controlled generalized CNN cells, while the stability of the circuit is studied by determining the eigenvalues of the stability matrices, the dynamics as well as onset of chaos, torus and bifurcation have been investigated through laboratory hardware experiments and numerical analysis of the generalized SC-CNN equations. The experimental results such as phase portraits, Poincaré map and power spectra are in good agreement with those of numerical computations. We further validate our findings with data obtained from both experimental time series observations and numerical simulations and discuss "0-1 test" for distinguishing quasiperiodicity and chaoticity, which successfully detects the transition. The results obtained are quite satisfactory and significant.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

An Experimental Study of the Forced Response of Pre- and Post-Critical Plates

1995 ◽  
Author(s):  
Kevin D. Murphy ◽  
Lawrence N. Virgin ◽  
Stephen A. Rizzi
Keyword(s):  
Experimental Study ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Small Amplitude ◽  
Narrow Band ◽  
Power Spectra ◽  
Forced Response ◽  
Acoustic Excitation ◽  
Rectangular Plates ◽  
Auto Correlation

Abstract Experimental results are presented which characterize the dynamic response of homogeneous, fully clamped, rectangular plates to narrow band acoustic excitation and uniform thermal loads. Using time series, pseudo-phase projections, power spectra and auto-correlation functions, small amplitude vibrations are considered about both the pre- and post-critical states. These techniques are then employed to investigate the snap-through response. The results for snap-through suggest that the motion is temporally complex and a Lyapunov exponent calculation confirms that the motion is chaotic. Finally, a snap-through boundary is mapped in the (ω, SPL) parameter space separating the regions of snap-through and no snap-through.

scholarly journals Determination of the complex frequencies for the normal modes below 1mHz after the 2010 Maule and 2011 Tohoku earthquakes

2014 ◽  
Vol 56 (5) ◽  
Author(s):  
Hao Ding ◽  
Wen-Bin Shen
Keyword(s):  
Time Series ◽  
Normal Modes ◽  
Power Spectra ◽  
Tohoku Earthquake ◽  
Superconducting Gravimeter ◽  
Width Ratio ◽  
Maule Earthquake ◽  
Attenuation Models ◽  
First Time

<p>Based upon SG (superconducting gravimeter) records, the autoregressive method proposed by Chao and Gilbert [1980] is used to determine the frequencies of the singlets of seven spheroidal modes (<sub>0</sub>S<sub>2</sub>, <sub>2</sub>S<sub>1</sub>, <sub>0</sub>S<sub>3</sub>, <sub>0</sub>S<sub>4</sub>, <sub>1</sub>S<sub>2</sub>, <sub>0</sub>S<sub>0</sub>, and <sub>3</sub>S<sub>1</sub>) and the degenerate frequencies of three toroidal modes (<sub>0</sub>T<sub>2</sub>, <sub>0</sub>T<sub>3</sub>, and <sub>0</sub>T<sub>4</sub>) below 1 mHz after two recent huge earthquakes, the 2010 Mw8.8 Maule earthquake and the 2011 Mw9.1 Tohoku earthquake. The corresponding quality factor <em>Q</em>s are also determined for those modes, of which the <em>Q</em>s of the five singlets of <sub>1</sub>S<sub>2</sub> and the five singlets (<em>m</em>=0, <em>m</em>=±2, and <em>m</em>=±3) of <sub>0</sub>S<sub>4</sub> are estimated for the first time using the SG observations. The singlet <em>m</em>=0 of <sub>3</sub>S<sub>1</sub> is clearly observed from the power spectra of the SG time series without using other special spectral analysis methods or special time series from pole station records. In addition, the splitting width ratio <em>R</em> of <sub>3</sub>S<sub>1</sub> is 0.99, and consequently we conclude that <sub>3</sub>S<sub>1</sub> is normally split. The frequencies and <em>Q</em>s of the modes below 1mHz may contribute to refining the 3D density and attenuation models of the Earth.</p>

scholarly journals Determination of the Starting Point in Time Series for Trend Detection Based on Overlapping Trend

2016 ◽  
Vol 16 (6) ◽  
pp. 98-110
Author(s):  
Gao Xuedong ◽  
Gu Kan
Keyword(s):  
Time Series ◽  
Piecewise Linear ◽  
Negative Influence ◽  
Trend Detection ◽  
Computational Accuracy ◽  
Starting Point ◽  
Time Series Studies ◽  
Definition Of ◽  
Stage Characteristic

Abstract The traditional time series studies consider the time series as a whole while carrying on the trend detection; therefore not enough attention is paid to the stage characteristic. On the other hand, the piecewise linear fitting type methods for trend detection are lacking consideration of the possibility that the same node belongs to multiple trends. The above two methods are affected by the start position of the sequence. In this paper, the concept of overlapping trend is proposed, and the definition of milestone nodes is given on its base; these way not only the recognition of overlapping trend is realized, but also the negative influence of the starting point of sequence is effectively reduced. The experimental results show that the computational accuracy is not affected by the improved algorithm and the time cost is greatly reduced when dealing with the processing tasks on dynamic growing data sequence.

scholarly journals Wavelet analysis applied on temporal data sets in order to reveal possible pre-seismic radio anomalies and comparison with the trend of the raw data 

2021 ◽  
Author(s):  
Giovanni Nico ◽  
Pier Francesco Biagi ◽  
Anita Ermini ◽  
Mohammed Yahia Boudjada ◽  
Hans Ulrich Eichelberger ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Analysis ◽  
Power Spectrum ◽  
Power Spectra ◽  
Wavelet Spectrum ◽  
Time Signal ◽  
Time Behavior ◽  
Sudden Increase ◽  
Night Time ◽  
Raw Data

&lt;p&gt;Since 2009, several radio receivers have been installed throughout Europe in order to realize the INFREP European radio network for studying the VLF (10-50 kHz) and LF (150-300 kHz) radio precursors of earthquakes. Precursors can be related to &amp;#8220;anomalies&amp;#8221; in the night-time behavior of&amp;#160; VLF signals. A suitable method of analysis is the use of the Wavelet spectra.&amp;#160; Using the &amp;#8220;Morlet function&amp;#8221;, the Wavelet transform of a time signal is a complex series that can be usefully represented by its square amplitude, i.e. considering the so-called Wavelet power spectrum.&lt;/p&gt;&lt;p&gt;The power spectrum is a 2D diagram that, once properly normalized with respect to the power of the white noise, gives information on the strength and precise time of occurrence of the various Fourier components, which are present in the original time series. The main difference between the Wavelet power spectra and the Fourier power spectra for the time series is that the former identifies the frequency content along the operational time, which cannot be done with the latter. Anomalies are identified as regions of the Wavelet spectrogram characterized by a sudden increase in the power strength.&lt;/p&gt;&lt;p&gt;On January 30, 2020 an earthquake with Mw= 6.0 occurred in Dodecanese Islands. The results of the Wavelet analysis carried out on data collected some INFREP receivers is compared with the trends of the raw data. The time series from January 24, 2020 till January 31, 2000 was analyzed. The Wavelet spectrogram shows a peak corresponding to a period of 1 day on the days before January 30. This anomaly was found for signals transmitted at the frequencies 19,58 kHz, 20, 27 kHz, 23,40 kHz with an energy in the peak increasing from 19,58 kHz to 23,40 kHz. In particular, the signal at the frequency 19,58 kHz, shows a peak on January 29, while the frequencies 20,27 kHz and 23,40 kHz are characterized by a peak starting on January 28 and continuing to January 29. The results presented in this work shows the perspective use of the Wavelet spectrum analysis as an operational tool for the detection of anomalies in VLF and LF signal potentially related to EQ precursors.&lt;/p&gt;

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