RESONANCE PATTERNS IN ONE-DIMENSIONAL ARRAYS OF COUPLED NONLINEAR EXCITABLE SYSTEMS

1994 ◽  
Vol 04 (06) ◽  
pp. 1631-1638 ◽  
Author(s):  
V. PÉREZ-MUÑUZURI ◽  
M. ALONSO ◽  
L.O. CHUA ◽  
V. PÉREZ-VILLAR
Keyword(s):  
Coupling Strength ◽  
Signal Transmission ◽  
Periodic Wave ◽  
Excitable Cells ◽  
Nonmonotonic Dependence ◽  
One Dimensional ◽  
Locking Range ◽  
Excitable Systems ◽  
Wave Trains ◽  
Coupling Strengths

Periodical signal transmission of waves through a one-dimensional array of coupled nonlinear electronic excitable cells have been investigated experimentally. Periodic wave trains give rise to a full devil’s staircase. The dependence of firing numbers defined for an excitable medium, on the amplitude and frequency of forcing, excitability of the medium, and coupling strength between cells is investigated. A nonmonotonic dependence between the locking range and the excitability has been observed for various n:m resonance regions, for different coupling strengths.

ROLE OF REFRACTORY PERIOD IN HOMOCLINIC MODELS OF NEURAL SYNCHRONIZATION

2007 ◽  
Vol 17 (02) ◽  
pp. 79-86 ◽  
Author(s):  
A. MONTINA ◽  
C. MENDOZA ◽  
F. T. ARECCHI
Keyword(s):  
Response Time ◽  
Coupling Strength ◽  
Signal Strength ◽  
One Dimensional ◽  
Intermittent Behavior ◽  
Excitable Systems ◽  
Sudden Transition ◽  
A Site ◽  
External Signals

We study the properties of a homoclinic model of neuron by introducing a suitable one-dimensional map. We show that the system is characterized by a response time to external signals which is a decreasing function of the signal strength, in contrast to excitable models whose response time is signal-independent. In a one-dimensional array of these systems with bidirectional coupling, we observe a sudden transition to a synchronized state at a certain value of the coupling strength. The transition occurs when the response time of a site to the signals of the adjacent sites is of the order of refractory time. Near the transition, we find an intermittent behavior due to the competition between a turbulent and a synchronized state. The observed behavior distinguishes homoclinic systems from excitable systems.

Entrainment and Annihilation of Reentrant Excitation in a Periodically Stimulated Ring of Excitable Media

1997 ◽  
Vol 36 (04/05) ◽  
pp. 290-293
Author(s):  
L. Glass ◽  
T. Nomura
Keyword(s):  
Cardiac Arrhythmias ◽  
Initial Phase ◽  
Human Heart ◽  
Periodic Wave ◽  
Excitable Media ◽  
One Dimensional ◽  
Clinical Observations ◽  
Periodic Stimulation ◽  
Reentrant Excitation ◽  
Stimulation Of

Abstract:Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.

Stability of periodic waves in shallow water

1974 ◽  
Vol 66 (1) ◽  
pp. 81-96 ◽  
Author(s):  
P. J. Bryant
Keyword(s):  
Shallow Water ◽  
Wave Train ◽  
Periodic Wave ◽  
Fundamental Wave ◽  
Cnoidal Waves ◽  
Margin Of Stability ◽  
Fundamental Wavelength ◽  
Stokes Waves ◽  
Wave Trains ◽  
Permanent Shape

Waves of small but finite amplitude in shallow water can occur as periodic wave trains of permanent shape in two known forms, either as Stokes waves for the shorter wavelengths or as cnoidal waves for the longer wavelengths. Calculations are made here of the periodic wave trains of permanent shape which span uniformly the range of increasing wavelength from Stokes waves to cnoidal waves and beyond. The present investigation is concerned with the stability of such permanent waves to periodic disturbances of greater or equal wavelength travelling in the same direction. The waves are found to be stable to infinitesimal and to small but finite disturbances of wavelength greater than the fundamental, the margin of stability decreasing either as the fundamental wave becomes more nonlinear (i.e. contains more harmonics), or as the wavelength of the periodic disturbance becomes large compared with the fundamental wavelength. The decreasing margin of stability is associated with an increasing loss of spatial periodicity of the wave train, to the extent that small but finite disturbances can cause a form of interaction between consecutive crests of the disturbed wave train. In such a case, a small but finite disturbance of wavelength n times the fundamental wavelength converts the wave train into n interacting wave trains. The amplitude of the disturbance subharmonic is then nearly periodic, the time scale being the time taken for repetitions of the pattern of interactions. When the disturbance is of the same wavelength as the permanent wave, the wave is found to be neutrally stable both to infinitesimal and to small but finite disturbances.

EVOLUTION OF ATOM-FIELD PROBABILITY IN A COUPLED CAVITY SYSTEM

2013 ◽  
Vol 22 (03) ◽  
pp. 1350029
Author(s):  
K. V. PRIYESH ◽  
RAMESH BABU THAYYULLATHIL
Keyword(s):  
Coupling Strength ◽  
Probability Amplitude ◽  
Field Coupling ◽  
Level Atom ◽  
Cavity System ◽  
Coupling Strengths ◽  
Field Excitation ◽  
Excitation Probability ◽  
Hopping Strength ◽  
Coupled Cavity

In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.

Signal Propagation Along Unidimensional Neuronal Networks

2005 ◽  
Vol 94 (5) ◽  
pp. 3406-3416 ◽  
Author(s):  
Ofer Feinerman ◽  
Menahem Segal ◽  
Elisha Moses
Keyword(s):  
Large Scale ◽  
Signal Transmission ◽  
Signal Propagation ◽  
High Amplitude ◽  
Adhesive Material ◽  
One Dimensional ◽  
Calcium Indicator ◽  
Scale Population ◽  
Population Burst ◽  
Linear Signal

Dissociated neurons were cultured on lines of various lengths covered with adhesive material to obtain an experimental model system of linear signal transmission. The neuronal connectivity in the linear culture is characterized, and it is demonstrated that local spiking activity is relayed by synaptic transmission along the line of neurons to develop into a large-scale population burst. Formally, this can be treated as a one-dimensional information channel. Directional propagation of both spontaneous and stimulated bursts along the line, imaged with the calcium indicator Fluo-4, revealed the existence of two different propagation velocities. Initially, a small number of neighboring neurons fire, leading to a slow, small and presumably asynchronous wave of activity. The signal then spontaneously develops to encompass much larger and further populations, and is characterized by fast propagation of high-amplitude activity, which is presumed to be synchronous. These results are well described by an existing theoretical framework for propagation based on an integrate-and-fire model.

scholarly journals Distinguishing f(R) gravity with cosmic voids

2014 ◽  
Vol 11 (S308) ◽  
pp. 589-590 ◽  
Author(s):  
P. Zivick ◽  
P. M. Sutter
Keyword(s):  
Coupling Strength ◽  
Significant Shift ◽  
Initial Estimate ◽  
Galaxy Surveys ◽  
The Public ◽  
Coupling Strengths ◽  
Cosmic Voids

AbstractWe use properties of void populations identified in N-body simulations to forecast the ability of upcoming galaxy surveys to differentiate models of f(R) gravity from \lcdm cosmology. We analyze simulations designed to mimic the densities, volumes, and clustering statistics of upcoming surveys, using the public {\tt VIDE} toolkit. We examine void abundances as a basic probe at redshifts 1.0 and 0.4. We find that stronger f(R) coupling strengths produce voids up to ∼20% larger in radius, leading to a significant shift in the void number function. As an initial estimate of the constraining power of voids, we use this change in the number function to forecast a constraint on the coupling strength of Δ fR0 = 10-5.

Electron-Phonon Coupling Strength of Specific Phonons from First Principles Lapw Calculations

1988 ◽  
Vol 141 ◽  
Author(s):  
H. Krakauer ◽  
R. E. Cohen ◽  
W. E. Pickett
Keyword(s):  
Coupling Strength ◽  
First Principles ◽  
Mode Coupling ◽  
Local Density ◽  
Matrix Elements ◽  
Dual Representation ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Coupling Strengths ◽  
The Difference

AbstractElectron-phonon matrix elements, phonon linewidths and mode coupling strengths are being calculated for La2-xMxCuO4 (M-divalent cation, for paramagnetic x-0.0 and for x-0.15 in a rigid band picture) from first principles local density calculations. The change in potential due to a particular phonon mode is calculated from the difference of self-consistent one-electron potentials, and appropriate Fermi surface averages are carried out for selected modes, allowing us to obtain the phonon linewidth due to the electron-phonon interaction, and the corresponding coupling strength λQ. Here we establish the numerical accuracy within the dual representation of the potential used in the Linearized Augmented Plane Wave (LAPW) method. Evaluations of phonon linewidths and mode coupling strengths are presented for Al and Nb and compared with previous information on these modes. We present preliminary results for the full matrix elements and coupling of the La2CuO4 oxygen planar X-point breathing mode, and compare with a simpler approximation.

scholarly journals Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons

2007 ◽  
Vol 19 (11) ◽  
pp. 3011-3050 ◽  
Author(s):  
Andreas Kaltenbrunner ◽  
Vicenç Gómez ◽  
Vicente López
Keyword(s):  
Phase Transition ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Stochastic Dynamics ◽  
Upper And Lower Bounds ◽  
Critical Coupling ◽  
Sustained Activity ◽  
Large Ensembles ◽  
Coupling Strengths ◽  
Pulse Coupled Oscillators

An ensemble of stochastic nonleaky integrate-and-fire neurons with global, delayed, and excitatory coupling and a small refractory period is analyzed. Simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength. Below the critical coupling production of spikes in the ensemble is governed by the stochastic dynamics, whereas for coupling greater than the critical value, the stochastic dynamics loses its influence and the units organize into several clusters with self-sustained activity. All units within one cluster spike in unison, and the clusters themselves are phase-locked. Theoretical analysis leads to upper and lower bounds for the average interspike interval of the ensemble valid for all possible coupling strengths. The bounds allow calculating the limit behavior for large ensembles and characterize the phase transition analytically. These results may be extensible to pulse-coupled oscillators.

scholarly journals TRANSITION TO CHAOTIC PHASE SYNCHRONIZATION THROUGH RANDOM PHASE JUMPS

2000 ◽  
Vol 10 (11) ◽  
pp. 2533-2539 ◽  
Author(s):  
D. PAZÓ ◽  
I. P. MARIÑO ◽  
V. PÉREZ-VILLAR ◽  
V. PÉREZ-MUÑUZURI
Keyword(s):  
Diffusion Model ◽  
Coupling Strength ◽  
Brownian Dynamics ◽  
Phase Synchronization ◽  
Random Phase ◽  
Random Generation ◽  
Stochastic Diffusion ◽  
One Dimensional

Phase synchronization is shown to occur between opposite cells of a ring consisting of chaotic Lorenz oscillators coupled unidirectionally through driving. As the coupling strength is diminished, full phase synchronization cannot be achieved due to random generation of phase jumps. The Brownian dynamics underlying this process is studied in terms of a stochastic diffusion model of a particle in a one-dimensional medium.

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