AN EXPERIMENTAL STUDY OF A POPULATION OF RELAXATION OSCILLATORS WITH A PHASE-REPELLING MEAN-FIELD COUPLING

1996 ◽  
Vol 06 (07) ◽  
pp. 1211-1253 ◽  
Author(s):  
ADAM A. BRAILOVE ◽  
PAUL S. LINSAY
Keyword(s):  
Exponential Distribution ◽  
Dynamical Behavior ◽  
Mean Field ◽  
Transient Behavior ◽  
Geometrical Model ◽  
The Novel ◽  
Op Amp ◽  
Relaxation Oscillators ◽  
Field Coupling ◽  
Simple Geometrical Model

The dynamical behavior of a system of coupled relaxation oscillators is studied experimentally. A population of up to 15 coupled electronic op-amp relaxation oscillators is used as a prototype for the real collections of limit-cycle oscillators frequently found in many physical, biological, and technological systems. The oscillators interact via an all-to-all or mean-field coupling. The rarely studied case of antiferromagnetic interactions, in which oscillators tend to repel each other in phase, is considered. The behavior of the system is significantly different from the predictions of the limited theory that is currently available. The novel behavior observed includes the existence of numerous distinguishable phase-locked states and an exponential distribution of the duration of transients. The critical coupling strength necessary for the oscillator system to completely phase-lock is measured. A simple geometrical model of the dynamics of the system during the transient is presented as a means of understanding the exponential distribution of transient lengths. In addition, a phase-response oscillator model is shown to exhibit similar transient behavior.

BURSTING TYPES AND STABLE DOMAINS OF RULKOV NEURON NETWORK WITH MEAN FIELD COUPLING

2013 ◽  
Vol 23 (12) ◽  
pp. 1330041 ◽  
Author(s):  
HONGJUN CAO ◽  
YANGUO WU
Keyword(s):  
Parameter Space ◽  
Single Neuron ◽  
Complex Dynamics ◽  
Mean Field ◽  
Flip Bifurcation ◽  
Neuron Network ◽  
Square Wave ◽  
Field Coupling ◽  
The Mean ◽  
Stable Domains

Based on the detailed bifurcation analysis and the master stability function, bursting types and stable domains of the parameter space of the Rulkov map-based neuron network coupled by the mean field are taken into account. One of our main findings is that besides the square-wave bursting, there at least exist two kinds of triangle burstings after the mean field coupling, which can be determined by the crisis bifurcation, the flip bifurcation, and the saddle-node bifurcation. Under certain coupling conditions, there exists two kinds of striking transitions from the square-wave bursting (the spiking) to the triangle bursting (the square-wave bursting). Stable domains of fixed points, periodic solutions, quasiperiodic solutions and their corresponding firing regimes in the parameter space are presented in a rigorous mathematical way. In particular, as a function of the intrinsic control parameters of each single neuron and the external coupling strength, a stable coefficient of the Neimark–Sacker bifurcation is derived in a parameter plane. These results show that there exist complex dynamics and rich firing regimes in such a simple but thought-provoking neuron network.

scholarly journals Nova Cygni 1975: A Model for the Variability of the 3 Hour Period

1977 ◽  
Vol 42 ◽  
pp. 311-312
Author(s):  
A.C. Fabian ◽  
J. E. Pringle
Keyword(s):  
Orbital Period ◽  
Geometrical Model ◽  
Period Variation ◽  
Periodic Modulation ◽  
Azimuthal Variation ◽  
Simple Geometrical Model ◽  
Optical Flux ◽  
The Continuum

A periodic modulation in the optical flux from Nova Cygni 1975 has been observed since shortly after outburst (Tempesti 1975) and the period is known to have varied by at least a few percent (Semeniuk et al. 1976). We account for the modulation in terms of a simple geometrical model in which the wind emanating from the nova is shadowed by its binary companion (see Fabian and Pringle 1977 for a fuller account). This produces an azimuthal variation in the radius of the surface of last scattering, RS, which an observer sees as a periodic modulation of the. continuum with period roughly equal to the orbital period. Variation of the observed period is accounted for in terms of variation of the size of RS.

Experimental determination of the instrumental transparency function of texture goniometers

2000 ◽  
Vol 33 (4) ◽  
pp. 1162-1174 ◽  
Author(s):  
K. Moras ◽  
A. H. Fischer ◽  
H. Klein ◽  
H. J. Bunge
Keyword(s):  
Pole Figure ◽  
Silicon Crystal ◽  
Window Size ◽  
Geometrical Model ◽  
Bragg Angle ◽  
Rocking Curve ◽  
Order Of Magnitude ◽  
Simple Geometrical Model ◽  
Position Sensitive Detectors

The instrumental transparency functions of five commercially available texture goniometers were measured experimentally with six monocrystalline samples cut in different orientations from a large highly perfect silicon crystal with a rocking curve of less than 0.01°. Transparency functions were measured in steps of 0.02 to 0.2° in the pole-figure angles α, β. The window size Δα depends on the Bragg angle θ in the form 1/sinθ; the window size Δω is constant for each goniometer. The dominant instrumental parameter determining the long axis Δα of the pole-figure window is the axial width of the detector entrance slit. This parameter is smallest for area detectors (smaller by more than an order of magnitude compared with conventional scintillation detectors as well as one-dimensional position-sensitive detectors). The main features of the pole-figure window and their dependence on the instrumental parameters can be deduced fairly well from a simple geometrical model. The particular shapes of the transparency functions of the studied goniometers are markedly different. Particularly, they are not very well represented by Gauss functions. The two-dimensional transparency function can be fairly well characterized by its α and β profiles. The normalized profiles are virtually independent of the goniometer angles 2θ and α. The increasing size of the pole-figure window with decreasing θ puts a lower limit on the Bragg angle below which pole-figure measurement ceases to be meaningful.

scholarly journals Analysis, adaptive control and circuit simulation of a novel finance system with dissaving

2016 ◽  
Vol 26 (1) ◽  
pp. 95-115 ◽  
Author(s):  
Ourania I. Tacha ◽  
Christos K. Volos ◽  
Ioannis N. Stouboulos ◽  
Ioannis M. Kyprianidis
Keyword(s):  
Adaptive Control ◽  
Nonlinear Theory ◽  
Circuit Simulation ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
The Novel ◽  
Finance System ◽  
Simulation Tools

In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

AGING IN A ONE-DIMENSIONAL EDWARDS–ANDERSON SPIN GLASS MODEL WITH LONG-RANGE INTERACTIONS

2003 ◽  
Vol 14 (03) ◽  
pp. 257-265 ◽  
Author(s):  
MARCELO A. MONTEMURRO ◽  
FRANCISCO A. TAMARIT
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Dynamical Behavior ◽  
Mean Field ◽  
Dimensional System ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Glass Model ◽  
The One ◽  
Aging Phenomena

In this work we study, by means of numerical simulations, the out-of-equilibrium dynamics of the one-dimensional Edwards–Anderson model with long-range interactions of the form ± Jr-α. In the limit α → 0 we recover the well known Sherrington–Kirkpatrick mean-field version of the model, which presents a very complex dynamical behavior. At the other extreme, for α → ∞ the model converges to the nearest-neighbor one-dimensional system. We focus our study on the dependence of the dynamics on the history of the sample (aging phenomena) for different values of α. The model is known to have mean-field exponents already for values of α = 2/3. Our results indicate that the crossover to the dynamic mean-field occurs at a value of α < 2/3.

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