scholarly journals HOW CRUCIAL IS SMALL WORLD CONNECTIVITY FOR DYNAMICS?

2006 ◽  
Vol 16 (09) ◽  
pp. 2767-2775 ◽  
Author(s):  
PRASHANT M. GADE ◽  
SUDESHNA SINHA
Keyword(s):  
Spectral Properties ◽  
Chaotic Systems ◽  
Signal To Noise Ratio ◽  
Dynamical Behavior ◽  
Small World ◽  
High Strength ◽  
Nonlocal Coupling ◽  
Small Noise ◽  
Optimal Value ◽  
Neuronal Systems

We study the dynamical behavior of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties occur only at a reasonably high strength of nonlocal coupling. Further, spectral features, such as signal-to-noise ratio (SNR), change monotonically with respect to the fraction of random rewiring, i.e. there is no optimal value of the rewiring fraction for which spectral properties are most pronounced. We also observe that for small rewiring, results are similar to those obtained by adding small noise.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

Tensile and wear behaviour of friction stir welded AA5052 and AA6101-T6 aluminium alloys: effect of welding parameters

2020 ◽  
Vol 117 (4) ◽  
pp. 405 ◽  
Author(s):  
G. Kasirajan ◽  
Sathish Rengarajan ◽  
R. Ashok kumar ◽  
G.R. Raghav ◽  
V.S. Rao ◽  
...  
Keyword(s):  
Strain Hardening ◽  
Aluminium Alloys ◽  
Signal To Noise Ratio ◽  
High Strength ◽  
High Heat ◽  
Wear Behaviour ◽  
Welding Parameters ◽  
Wear Properties ◽  
Friction Stir ◽  
Four Levels

To improve the performance and effectiveness of cost, constructing lightweight structure is the important factor for automobile, naval and aerospace industries. AA5052 and AA6101-T6 aluminium alloys are widely applied in transport industries, due to their lightweight and high strength and hence, joining of these two are unavoidable. Friction stir welding is an unconventional welding method, which is developed for constructing lightweight structures. This work describes the detailed study of friction stir welded dissimilar AA5052 and AA6101-T6 alloys. AA5052 and AA6101-T6 plates are welded with rotation rates of 765–1400 rpm and offset distances at advancing side of 0–2 mm. For this purpose, four levels of welding parameters based on Taguchi L16 orthogonal array are chosen. To determine the optimum combinational levels and identify the effect of above-mentioned parameters on tensile and wear properties, Signal to Noise ratio and ANOVA respectively are used. From the results, it is observed that the combination of 1 mm offset distance at advancing side and 1400 rpm rotating speed produces better tensile and wear properties, which is due to high heat generation, sufficient flow of materials and balanced precipitation and strain hardening effects. On the other hand, the combination of 2 mm tool offset at advancing side and 765 rpm rotational rate exhibits poor properties, which is associated with low heat input, defects formation, precipitate coarsening and lesser strain hardening effects.

SPECTRAL PROPERTIES OF AN ELASTIC ROD-SPRING COUPLED SYSTEM IMMERSED IN A FLUID

1992 ◽  
Vol 02 (04) ◽  
pp. 441-460 ◽  
Author(s):  
J. SANCHEZ-HUBERT ◽  
S. BÉRÉTÉ ◽  
J. PLANCHARD
Keyword(s):  
Heat Exchangers ◽  
Spectral Properties ◽  
Nuclear Reactor ◽  
Dynamical Behavior ◽  
Coupled System ◽  
Elastic Tube ◽  
Elastic Rod ◽  
Resonance Frequencies ◽  
Continuous Material ◽  
Very High

The study of vibrations of elastic tube bundles immersed in a fluid is very important in Engineering, for example concerning the dynamical behavior of heat exchangers, nuclear reactor cores, etc. This paper is concerned with the investigation of the resonance frequencies when the number of rods is very high. That requires us to use the homogenization technique for modelling this coupled system by an equivalent continuous material. We then show that this equivalent system may have an essential spectrum.

scholarly journals Phase diffusion and the small-noise approximation in linear amplifiers: Limitations and beyond

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 200 ◽  
Author(s):  
Andy Chia ◽  
Michal Hajdušek ◽  
Rosario Fazio ◽  
Leong-Chuan Kwek ◽  
Vlatko Vedral
Keyword(s):  
Signal To Noise Ratio ◽  
Noise Analysis ◽  
Photon Number ◽  
Optical Field ◽  
Signal To Noise ◽  
Small Noise ◽  
Phase Diffusion ◽  
Small Noise Approximation ◽  
Linear Amplifier ◽  
Phase Uncertainty

The phase of an optical field inside a linear amplifier is widely known to diffuse with a diffusion coefficient that is inversely proportional to the photon number. The same process occurs in lasers which limits its intrinsic linewidth and makes the phase uncertainty difficult to calculate. The most commonly used simplification is to assume a narrow photon-number distribution for the optical field (which we call the small-noise approximation). For coherent light, this condition is determined by the average photon number. The small-noise approximation relies on (i) the input to have a good signal-to-noise ratio, and (ii) that such a signal-to-noise ratio can be maintained throughout the amplification process. Here we ask: For a coherent input, how many photons must be present in the input to a quantum linear amplifier for the phase noise at the output to be amenable to a small-noise analysis? We address these questions by showing how the phase uncertainty can be obtained without recourse to the small-noise approximation. It is shown that for an ideal linear amplifier (i.e. an amplifier most favourable to the small-noise approximation), the small-noise approximation breaks down with only a few photons on average. Interestingly, when the input strength is increased to tens of photons, the small-noise approximation can be seen to perform much better and the process of phase diffusion permits a small-noise analysis. This demarcates the limit of the small-noise assumption in linear amplifiers as such an assumption is less true for a nonideal amplifier.

Chaotic burst synchronization in a two-small-world-layer neuronal network

2015 ◽  
Vol 26 (05) ◽  
pp. 1550051 ◽  
Author(s):  
Yanhong Zheng ◽  
Haixia Wang
Keyword(s):  
Neuronal Network ◽  
Coupling Strength ◽  
Small World ◽  
Interlayer Coupling ◽  
The Other ◽  
Spatiotemporal Pattern ◽  
Small Noise ◽  
Irregular Pattern ◽  
Burst Synchronization ◽  
Chaotic Burst

Chaotic burst synchronization in a two-small-world-layer neuronal network is studied in this paper. For a neuronal network coupled by two single-small-world-layer networks with link probability differences between layers, the two-layer network can achieve synchrony as the interlayer coupling strength increases. When chaotic layer network is coupled with chaotic-burst-synchronization layer network, the latter is dominant at small interlayer coupling strength, so it can make the layer with the irregular pattern show some regular and also exhibit the same pattern with the other layer. However, when chaotic layer is coupled with firing synchronization layer, the ordered layer is dominated by a disordered one with the interlayer coupling strength increasing. When the interlayer coupling strength is large enough, both networks are chaotic burst synchronization. Therefore, the synchronous states strongly depend on the interlayer coupling strength and the link probability. Moreover, the spatiotemporal pattern synchronization between the networks is robust to small noise.

scholarly journals On the Caputo-Fabrizio fractal fractional representation for the Lorenz chaotic system

2021 ◽  
Vol 6 (11) ◽  
pp. 12395-12421
Author(s):  
Anastacia Dlamini ◽  
◽  
Emile F. Doungmo Goufo ◽  
Melusi Khumalo
Keyword(s):  
Chaotic System ◽  
Fractional Derivatives ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Integral Operators ◽  
Fractional Dimension ◽  
Science And Engineering ◽  
Widespread Application ◽  
Lorenz Chaotic System

<abstract><p>The widespread application of chaotic dynamical systems in different fields of science and engineering has attracted the attention of many researchers. Hence, understanding and capturing the complexities and the dynamical behavior of these chaotic systems is essential. The newly proposed fractal-fractional derivative and integral operators have been used in literature to predict the chaotic behavior of some of the attractors. It is argued that putting together the concept of fractional and fractal derivatives can help us understand the existing complexities better since fractional derivatives capture a limited number of problems and on the other side fractal derivatives also capture different kinds of complexities. In this study, we use the newly proposed Caputo-Fabrizio fractal-fractional derivatives and integral operators to capture and predict the behavior of the Lorenz chaotic system for different values of the fractional dimension $ q $ and the fractal dimension $ k $. We will look at the well-posedness of the solution. For the effect of the Caputo-Fabrizio fractal-fractional derivatives operator on the behavior, we present the numerical scheme to study the graphical numerical solution for different values of $ q $ and $ k $.</p></abstract>

scholarly journals Impacts of autapse on chaotic resonance in single neurons and small-world neuronal networks

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
Veli Baysal ◽  
Erdem Erkan ◽  
Ergin Yilmaz
Keyword(s):  
Neuronal Networks ◽  
Single Neuron ◽  
Small World ◽  
Chaotic Signal ◽  
Pacemaker Activity ◽  
Chemical Synapse ◽  
Single Neurons ◽  
Theme Issue ◽  
Pacemaker Neurons ◽  
Neuronal Systems

Chaotic resonance (CR) is a new phenomenon induced by an intermediate level of chaotic signal intensity in neuronal systems. In the current study, we investigated the effects of autapse on the CR phenomenon in single neurons and small-world (SW) neuronal networks. In single neurons, we assume that the neuron has only one autapse modelled as electrical, excitatory chemical and inhibitory chemical synapse, respectively. Then, we analysed the effects of each one on the CR, separately. Obtained results revealed that, regardless of its type, autapse significantly increases the chaotic resonance of the appropriate autaptic parameter’s values. It is also observed that, at the optimal chaotic current intensity, the multiple CR emerges depending on autaptic time delay for all the autapse types when the autaptic delay time or its integer multiples match the half period or period of the weak signal. In SW networks, we investigated the effects of chaotic activity on the prorogation of pacemaker activity, where pacemaker neurons have different kinds of autapse as considered in single neuron cases. Obtained results revealed that excitatory and electrical autapses prominently increase the prorogation of pacemaker activity, whereas inhibitory autapse reduces or does not change it. Also, the best propagation was obtained when the autapse was excitatory. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

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