Statistics of Lifetimes for Transient Bursting States in Coupled Noisy Excitable Systems

2020 ◽  
Vol 15 (12) ◽  
Author(s):  
Nurtay Albanbay ◽  
Bekbolat Medetov ◽  
Michael A. Zaks
Keyword(s):  
Resting State ◽  
Additive Noise ◽  
External Noise ◽  
Electronic Circuits ◽  
Attraction Basin ◽  
Excitable Systems ◽  
Exponential Character ◽  
Large Ensembles ◽  
Intrinsic Fluctuations ◽  
Parameter Values

Abstract In ensembles of oscillators, intrinsic fluctuations often enable nontrivial dynamics in seemingly simple situations. One of such effects occurs in coupled FitzHugh–Nagumo oscillators subjected to external noise. At the considered parameter values, the global deterministic attractor is the resting state. Additive noise invokes transient bursting: series of intermittent patches of spikes, followed by the abrupt decay to rest. Duration of this transient, small for weak noise, asymptotically diverges when the noise becomes stronger. Remarkably, in repeated trials at fixed parameters, the number of bursts until the ultimate decay strongly varies. Lifetime statistics for this transient in large ensembles of numerical realizations features the exponential distribution. Observations on transient bursting are confirmed by experiments with coupled analog electronic circuits, modeling the FitzHugh–Nagumo dynamics. We relate the exponential character of the distribution to the probability that the system, disturbed by noise, escapes the local attraction basin of the resting state.

GLASSY DYNAMICS AT THE ONSET OF CHAOS WITH ADDITIVE NOISE

2005 ◽  
Vol 05 (02) ◽  
pp. L313-L318 ◽  
Author(s):  
FULVIO BALDOVIN ◽  
ALBERTO ROBLEDO
Keyword(s):  
Glass Transition ◽  
Transition Temperature ◽  
Additive Noise ◽  
Logistic Map ◽  
Supercooled Liquid ◽  
External Noise ◽  
Translation Invariance ◽  
Time Translation ◽  
Onset Of Chaos ◽  
Dynamical Properties

After recalling key phenomenological properties of glass formation, we point out that similar features are exhibited by the dynamical properties of the noise-perturbed iterates of the logistic map at the onset of chaos. The analysis includes two-step relaxation, aging, subdiffusion and arrest, as well as an expression analogous to the Adam–Gibbs relation connecting dynamical and thermodynamic properties of a glass former. The dynamical properties of the logistic map in the presence of external noise are seen to be comparable to those of a supercooled liquid above a glass transition temperature, whereas the noiseless attractor displays typical nonequilibrium aspects like loss of time translation invariance (aging). Reference is made to connections between the noiseless dynamics at the chaos threshold and the nonextensive formalism.

Experimental chaos from autonomous electronic circuits

1995 ◽  
Vol 353 (1701) ◽  
pp. 13-32 ◽  
Keyword(s):  
Steady State ◽  
State Space ◽  
Frequency Domain ◽  
Difference Equations ◽  
Measurement Techniques ◽  
Electronic Circuits ◽  
Chua’S Oscillator ◽  
State Behaviour ◽  
Parameter Values ◽  
Steady State Behaviour

Autonomous electronic circuits provide a convenient framework in which to study chaotic phenomena. These systems are easy to build, easy to measure, and easy to model using differential and difference equations. Furthermore, they operate in real time, and parameter values are readily adjusted. In this work, we discuss the nature of chaotic steady-state behaviour and describe how it manifests itself in autonomous electronic circuits. We study state space, time-and frequency-domain measurement techniques for characterizing steady-state behaviour. Because of its value as a paradigm for exploring chaos, we choose Chua’s oscillator as the vehicle for our experiments.

scholarly journals Modeling the Cytokine NetworkIn VitroandIn Vivo

2003 ◽  
Vol 5 (2) ◽  
pp. 93-110 ◽  
Author(s):  
Johannes Müller ◽  
Thorsten Tjardes
Keyword(s):  
Immune Response ◽  
Immune System ◽  
Resting State ◽  
Interleukin 1 ◽  
Innate Immune ◽  
Acquired Immunity ◽  
Planar System ◽  
System A ◽  
Clinical Pictures ◽  
Parameter Values

The present paper consist of two parts: in the first part an experiment investigating the endothelial cell/interleukin 1 system is analyzed by means of a model. The most interesting outcome is a bistability of the system: a small challenge will not lead to a reaction, while a challenge slightly above a certain threshold leads to a complete activation of the endothelial cells. This finding is used in the second part of the paper, where a caricature model of the innate immune response (the part of the immune system that is not based on acquired immunity) is described and analyzed. In this analysis, especially, the possible patterns of the dynamics in the absence of a challenge have been targeted. We find a variety of behaviors possible for the resulting planar system. For certain parameter values, a small challenge is ignored, while a challenge above a certain threshold leads to a massive strike of the immune system that comes eventually to rest again. Also bistability, periodic behavior or an unstable resting state can be found. It is heuristically possible to link most of these dynamical patterns with natural or pathological situations that can be found in clinical pictures.

scholarly journals Sex-specific Associations Between Traumatic Experiences and Resting-state Functional Connectivity in the Philadelphia Neurodevelopmental Cohort

2020 ◽  
Author(s):  
Shiying Wang ◽  
Jeffrey G. Malins ◽  
Heping Zhang ◽  
Jeffrey R. Gruen
Keyword(s):  
Functional Connectivity ◽  
Resting State ◽  
Traumatic Events ◽  
Traumatic Experiences ◽  
Resting State Networks ◽  
Functional Magnetic Resonance ◽  
Resting State Functional Connectivity ◽  
Intrinsic Connectivity ◽  
Parameter Values ◽  
Connectivity Distribution

AbstractBackgroundTraumatic experiences during childhood or adolescence are a significant risk factor for multiple psychiatric disorders and adversely affect cognitive functions. Resting-state functional magnetic resonance imaging has been used to investigate the effects of traumatic experiences on functional connectivity, but the impact of sex differences has not been well documented. This study investigated sex-specific associations between resting-state functional connectivity and traumatic experiences in typically developing youth.MethodsThe sample comprised 1395 participants, ages 8 to 21 years, from the Philadelphia Neurodevelopmental Cohort. Resting-state functional connectivity was characterized by voxel-wise intrinsic connectivity distribution parameter values derived from resting-state functional magnetic resonance imaging. Traumatic experiences were assessed based on a structured psychiatric evaluation. Sex, the number of traumatic events, and their interaction were regressed onto voxel-wise intrinsic connectivity distribution parameter values. Brain regions that passed cluster correction were used as seeds to define resting-state networks.ResultsAfter quality control, the final sample included 914 participants (mean (SD) age, 14.6 (3.3) years; 529 (57.8%) females; 437 (47.8%) experienced at least one kind of traumatic event). Four discrete anatomical clusters showed decreased functional connectivity as the number of traumatic events increased. The resting-state networks defined by using these four clusters as seeds corresponded with the somatomotor network. Sex-specific associations were identified in another four clusters for which males showed increased connectivity, and females showed decreased connectivity as the number of traumatic events increased. The resting-state networks defined by the four sex-specific clusters corresponded with the default mode network.ConclusionsTraumatic experiences are associated with an alteration of resting-state functional connectivity in the somatomotor network in youth without psychiatric diagnoses. The associations differ in direction between males and females in the default mode network, suggesting sex-specific responses to early exposure to trauma.

Coherence resonance in a chemical excitable system driven by coloured noise

2007 ◽  
Vol 366 (1864) ◽  
pp. 381-395 ◽  
Author(s):  
Valentina Beato ◽  
Irene Sendiña-Nadal ◽  
Ingeborg Gerdes ◽  
Harald Engel
Keyword(s):  
Correlation Time ◽  
Temporal Correlation ◽  
External Noise ◽  
Characteristic Time Scale ◽  
Noise Variance ◽  
Coherence Resonance ◽  
Uhlenbeck Process ◽  
Excitable Systems ◽  
Oregonator Model ◽  
Belousov Zhabotinsky Reaction

We investigate how the temporal correlation in excitable systems driven by external noise affects the coherence of the system's response. The coupling to the fluctuating environment is introduced via fluctuations of a bifurcation parameter that controls the local dynamics of the light-sensitive Belousov–Zhabotinsky reaction and of its numerical description, the Oregonator model. Both systems are brought from a highly incoherent regime to a coherent one by an appropriate choice of the correlation time and keeping noise variance constant. This effect has been found both for an Ornstein–Uhlenbeck process and for a dichotomous telegraph signal. In the latter case, we are able to connect the optimal correlation time, for which the system behaviour is most coherent, with a characteristic time scale of the system.

NOISE REDUCTION INDUCED BY EXTERNAL NOISE OR PERIODIC SIGNAL IN A DYNAMICAL SYSTEM

2001 ◽  
Vol 01 (03) ◽  
pp. L131-L138 ◽  
Author(s):  
SAUL L. GINZBURG ◽  
MARK A. PUSTOVOIT ◽  
OLEG V. GERASHCHENKO
Keyword(s):  
Dynamical System ◽  
Simple Model ◽  
Noise Reduction ◽  
Additive Noise ◽  
External Noise ◽  
Model System ◽  
Periodic Signal ◽  
Noise Sources ◽  
Analog Simulation ◽  
Simple Model System

We investigated, analytically and by analog simulation, a simple model system, an overdamped Kramers oscillator with two additive noise sources, internal white and external colored. We found that the magnetude of noise background in the spectrum of system outpit can decrease when the amplitude of external noise or periodic signal increases.

scholarly journals Lower Internal Additive Noise and Better Perceptual Template Characterize Binocular Contrast Sensitivity Summation

2021 ◽  
Vol 12 ◽  
Author(s):  
Pan Zhang ◽  
Hanlin Wang ◽  
Weicong Ren ◽  
Qing Lu ◽  
Chenxi Li ◽  
...  
Keyword(s):  
Contrast Sensitivity ◽  
Additive Noise ◽  
External Noise ◽  
Low Noise ◽  
Binocular Summation ◽  
Large Individual ◽  
Noise Levels ◽  
Large Individual Difference ◽  
Spatial Frequencies ◽  
Shed Light

Binocular summation is generally defined as the superiority of binocular over monocular performance. Here, we investigated how external noise modulates the effect of binocular summation on the contrast sensitivity function (CSF) and clarified the corresponding mechanisms with a perceptual template model (PTM). The contrast sensitivity (CS) over 10 spatial frequencies and three external noise levels was assessed under one binocular and two monocular viewing conditions. The binocular summation ratio (BSR) was calculated by dividing the area under the log CSF (AULCSF), or the CS of using both eyes, by that of only using the “good eye” (BSRG) or the “bad eye” (BSRB), respectively. We found that: (1) based on the AULCSF, the BSRB was higher than the BSRG; (2) based on the AULCSF, the BSR was more pronounced under zero-noise than under low-noise conditions, but the BSR was not higher than 1 under high-noise conditions due to a large individual difference; (3) based on the CS, with increasing spatial frequencies, the BSRB steadily increased; (4) both decreased internal additive noise and an improved perceptual template accounted for the gain in binocular summation. These results help us better understand the features of binocular CS and shed light on the clinical studies on populations with monocular CS loss.

COHERENT RESONANCE AND PHASE LOCKING IN NOISE-DRIVEN EXCITABLE SYSTEMS

2005 ◽  
Vol 19 (22) ◽  
pp. 3501-3509 ◽  
Author(s):  
XIAOQIN FENG ◽  
ZHIGANG ZHENG
Keyword(s):  
Spike Train ◽  
Natural Frequency ◽  
Phase Synchronization ◽  
Phase Locking ◽  
External Noise ◽  
Phase Dynamics ◽  
Synchronization Index ◽  
Excitable Systems ◽  
Coherent Resonance

The dynamical responses of an excitable FitzHugh–Nagumo (FHN) system under the drive of an external noise are studied. Noise can induce a sequence of firings. The n:m coherent resonance of the FHN oscillator with an intrinsic natural frequency is shown. This effect is discussed by resorting to the phase dynamics of a spike train and the phase synchronization index γnm.

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