OBSERVATIONS OF PHASE SYNCHRONIZATION PHENOMENA IN ONE-DIMENSIONAL ARRAYS OF COUPLED CHAOTIC ELECTRONIC CIRCUITS

2000 ◽  
Vol 10 (10) ◽  
pp. 2391-2398 ◽  
Author(s):  
ANDRZEJ DABROWSKI ◽  
ZBIGNIEW GALIAS ◽  
MACIEJ OGORZAŁEK
Keyword(s):  
Numerical Experiments ◽  
Phase Synchronization ◽  
Analytic Signal ◽  
Electronic Circuits ◽  
One Dimensional ◽  
Phase Plot ◽  
Chaotic Circuits ◽  
Signal Approach ◽  
Insight Into

Using numerical experiments we show that the phase synchronization concept enables better insight into the synchronization phenomena encountered in coupled nonlinear chaotic circuits. In some cases when the phase plot inspection does not allow to confirm synchrony such kind of behavior can be distinguished by inspection of the phase calculated using the analytic signal approach.

scholarly journals STUDY OF SYNCHRONIZED MOTIONS IN A ONE-DIMENSIONAL ARRAY OF COUPLED CHAOTIC CIRCUITS

1999 ◽  
Vol 09 (11) ◽  
pp. 2219-2224 ◽  
Author(s):  
ZBIGNIEW GALIAS ◽  
MACIEJ J. OGORZAŁEK
Keyword(s):  
Lyapunov Exponents ◽  
Coupling Strength ◽  
Numerical Experiments ◽  
Variational Equation ◽  
Electronic Circuits ◽  
One Dimensional ◽  
Synchronous Motion ◽  
Chaotic Circuits ◽  
The Stability ◽  
Theoretical Results

We investigate the stability of synchronous motion in an array of bidirectionally coupled electronic circuits. We compute Lyapunov exponents of the generic variational equation associated with directions transversal to the synchronization subspace. Using Lyapunov exponents we derive conditions for the coupling strength for which the stable synchronous solution exists. We also find the limit on the size of the network, which can sustain stable synchronous motion. Theoretical results are compared with the results of numerical experiments.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

scholarly journals Detection of Anomalous Diffusion with Deep Residual Networks

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 649
Author(s):  
Miłosz Gajowczyk ◽  
Janusz Szwabiński
Keyword(s):  
Image Classification ◽  
Anomalous Diffusion ◽  
Numerical Experiments ◽  
Driving Forces ◽  
Living Cells ◽  
Diffusion Type ◽  
Training Time ◽  
Initial Network ◽  
Unseen Data ◽  
Insight Into

Identification of the diffusion type of molecules in living cells is crucial to deduct their driving forces and hence to get insight into the characteristics of the cells. In this paper, deep residual networks have been used to classify the trajectories of molecules. We started from the well known ResNet architecture, developed for image classification, and carried out a series of numerical experiments to adapt it to detection of diffusion modes. We managed to find a model that has a better accuracy than the initial network, but contains only a small fraction of its parameters. The reduced size significantly shortened the training time of the model. Moreover, the resulting network has less tendency to overfitting and generalizes better to unseen data.

Time-dependent barrier passage of one-dimensional fractional damping reactive system

2018 ◽  
Vol 32 (26) ◽  
pp. 1850285
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qing ◽  
Yu-Qing Xu
Keyword(s):  
Transmission Coefficient ◽  
Brownian Particle ◽  
Time Dependent ◽  
Reactive System ◽  
Damping Properties ◽  
Flux Method ◽  
Fractional Damping ◽  
One Dimensional ◽  
Reactive Process ◽  
Insight Into

The time-dependent barrier passage of a Brownian particle diffusing in the fractional damping environment is studied by using the reactive flux method. Characteristic quantities such as the rate constant and stationary transmission coefficient are computed for a thimbleful of insight into the barrier escaping dynamics. Results show that the barrier recrossing of the fractional damping reactive system is obviously weakened. And the nonmonotonic varying of the stationary transmission coefficient reveals a close dependence of the escaping process on the fractional damping properties. The time-dependent barrier passage of one-dimensional fractional damping reactive process is found very similar to the two-dimensional non-Ohmic case.

ASYMPTOTICAL ANALYSIS OF ONE DIMENSIONAL GAS DYNAMICS EQUATIONS

2001 ◽  
Vol 6 (1) ◽  
pp. 117-128 ◽  
Author(s):  
A. Krylovas ◽  
R. Čiegis
Keyword(s):  
Gas Dynamics ◽  
Numerical Experiments ◽  
Method Of Averaging ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Resonance Case ◽  
Gas Dynamics Equations ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Asymptotical Analysis

A method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonance for periodic and almost periodic solutions are presented. In the resonance case the averaged system is solved numerically. Some results of numerical experiments are given.

Simple Chaotic Electronic Circuits

2011 ◽  
pp. 68-90
Author(s):  
M.P. Hanias ◽  
G. S. Tombras
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Critical State ◽  
Strange Attractors ◽  
Embedding Dimension ◽  
Kolmogorov Entropy ◽  
Electronic Circuits ◽  
Series Analysis ◽  
Chaotic Circuits

Simple chaotic electronics circuits as diode resonator circuits, Resistor-Inductor-LED optoelectronic chaotic circuits, and Single Transistor chaotic circuits can be used as transmitters and receivers for chaotic cryptosystems. In these circuits we can change and investigate the influence of various circuit parameters to the complexity of the so generated strange attractors. Time series analysis is performed following Grassberger and Procaccia’s method while invariant parameters as correlation, and minimum embedding dimension are respectively calculated. The Kolmogorov entropy is also calculated and the RLT circuits in a critical state are examined.

Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions

2012 ◽  
Vol 11 (3) ◽  
pp. 951-984 ◽  
Author(s):  
Dongsheng Yin ◽  
Chunxiong Zheng
Keyword(s):  
Fourier Transform ◽  
Coherent States ◽  
Numerical Experiments ◽  
Wave Length ◽  
Wave Functions ◽  
Parameter Recovery ◽  
Characteristic Wave ◽  
One Dimensional ◽  
Windowed Fourier Transform ◽  
Recovery Algorithm

AbstractThe coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper. The wave functions are assumed to oscillate on a characteristic wave length 0(ε) with ε ≪ 1. A parameter recovery algorithm is first developed for single-phased wave function based on a moment asymptotic analysis. This algorithm is then extended to multi-phased wave functions. If cross points or caustics exist, the coherent states approximation algorithm based on the parameter recovery will fail in some local regions. In this case, we resort to the windowed Fourier transform technique, and propose a composite coherent states approximation method. Numerical experiments show that the number of coherent states derived by the proposed method is much less than that by the direct windowed Fourier transform technique.

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