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At least 1,243 records · Page 69Linked to original sources
PubMed2002

Stochastic neural network model for spontaneous bursting in hippocampal slices.

A biologically plausible, stochastic, neural network model that exhibits spontaneous transitions between a low-activity (normal) state and a high-activity (epileptic) state is studied by computer simulation. Brief excursions of the network to the high-activity state lead to spontaneous population bursting similar to the behavior observed in hippocampal slices bathed in a high-potassium medium. Although the variability of interburst intervals in this model is due to stochasticity, first return maps of successive interburst intervals show trajectories that resemble the behavior expected near unstable periodic orbits (UPOs) of systems exhibiting deterministic chaos. Simulations of the effects of the application of chaos control, periodic pacing, and anticontrol to the network model yield results that are qualitatively similar to those obtained in experiments on hippocampal slices. Estimation of the statistical significance of UPOs through surrogate data analysis also leads to results that resemble those of similar analysis of data obtained from slice experiments and human epileptic activity. These results suggest that spontaneous population bursting in hippocampal slices may be a manifestation of stochastic bistable dynamics, rather than of deterministic chaos. Our results also question the reliability of some of the recently proposed, UPO-based, statistical methods for detecting determinism and chaos in experimental time-series data.

Action Potentials↗
PubMed2002

Stochastic synchronization in globally coupled phase oscillators.

Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.

Journal Article↗
PubMed2003

Piecewise linear differential equations and integrate-and-fire neurons: insights from two-dimensional membrane models.

We derive and study two-dimensional generalizations of integrate-and-fire models which can be found from a piecewise linear idealization of the FitzHugh-Nagumo or Morris-Lecar model. These models give rise to new properties not present in one-dimensional integrate-and-fire models. A detailed analytical study of the models is presented. In particular, (i) for the piecewise linear FitzHugh-Nagumo model, we determine analytically the bistability regime between stationary solutions and oscillations, that is, typical for class-II models. (ii) In the piecewise Morris-Lecar model, we find a noncanonical class-I transition from a stationary state to oscillations with logarithmic dependence similar to that found for leaky integrate-and-fire models. (iii) Furthermore, we establish a relation to the recently proposed resonate-and-fire model and show that a short input current pulse can trigger several spikes.

Journal Article↗
PubMed2003

Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance.

We show that a self-oscillatory system, driven at two frequencies close to that of the unforced system (resonance 1:1), becomes phase locked and exhibits two equivalent stable states of opposite phases. For spatially extended systems this phase bistability results in patterns characteristic for real order parameter systems, such as phase domains, labyrinths, and phase spatial solitons. In variational cases, the phase-locking mechanism is interpreted as a result of the periodic "rocking" of the system potential. Rocking could be tested experimentally in lasers and in oscillatory chemical reactions.

Journal Article↗
PubMed2003

Optically induced dynamics in nematic liquid crystals: the role of twist deformation and asymmetry.

We present a theoretical study of optically induced dynamics in a homeotropic nematic liquid crystal excited at normal incidence. By retaining the first symmetric and antisymmetric reorientation modes, the dynamical equations are reduced to a four-dimensional problem. The main advantage of this minimal approach is to emphasize the role of twisted mode and asymmetry of the light-induced molecular reorientation in a manner suitable for a clear physical interpretation. Theoretical results are compared with experiments in the particular case of circularly polarized light beams to show the physical origin of mode competition and of the breakdown of chiral and longitudinal symmetry. The model successfully describes previous experimental studies such as time-dependent three-dimensional molecular dynamics, light-induced stabilized helical reorientation, and in-plane precession regime in achiral nematics. While a recent experiment has revealed a new spatiotemporal transition, the model succeeds to describe all the features of such a bifurcation pointing out anew the importance of asymmetry. Finally, the first quantitative description of the appearance of a giant mirrorless optical bistability when twisted reorientation modes are excited is demonstrated. A qualitative physical interpretation is suggested for all these phenomena.

Journal Article↗
PubMed2003

Competition between electroconvection and Fréedericksz distortions in nematic liquid crystals with slightly positive dielectric anisotropy.

Planar electroconvection in nematic liquid crystals with positive dielectric anisotropy is theoretically studied in the nonlinear regime. The system is characterized by a competition between the nonequilibrium electroconvection instability and the equilibrium Fréedericksz distortions. Near a resulting multicritical bifurcation point a splay-roll instability and a bistability between the convective and the homogeneous states occur.

Journal Article↗
PubMed2003

McKean caricature of the FitzHugh-Nagumo model: traveling pulses in a discrete diffusive medium.

This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by the McKean caricature of the FitzHugh-Nagumo model. In the limit of a weak coupling strength, we construct the traveling wave solutions and obtain the critical coupling constant below which propagation failure occurs. We report the existence of two different pulse traveling waves with different propagation speeds. Analytical results on the wave speed are obtained. Earlier results on propagation in the bistable medium are found as a limiting regime of our analysis.

Journal Article↗
PubMed2003

Gain in stochastic resonance: precise numerics versus linear response theory beyond the two-mode approximation.

In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545-548; Fluct. Noise Lett. 1, L181 (2001)].

Journal Article↗
PubMed2003

Transitions across a barrier induced by deterministic forcings.

The response of a bistable dynamical system to a deterministic forcing is studied with emphasis on the kinetics of the passage across the barrier separating the two states, and compared to classical Kramers' theory describing the response to a Gaussian white noise forcing. The existence of nontrivial thresholds for the occurrence of transitions is established. Analytic results complemented by numerical simulations are derived for the characteristics of these transitions for periodic and chaotic forcings. The probabilistic properties of the response are finally addressed and some connections are established with the universal stable distributions of probability theory.

Journal Article↗
PubMed2003

Stochastic model for heart-rate fluctuations.

A normal human heart rate shows complex fluctuations in time, which is natural, because the heart rate is controlled by a large number of different feedback control loops. These unpredictable fluctuations have been shown to display fractal dynamics, long-term correlations, and 1/f noise. These characterizations are statistical and they have been widely studied and used, but much less is known about the detailed time evolution (dynamics) of the heart-rate control mechanism. Here we show that a simple one-dimensional Langevin-type stochastic difference equation can accurately model the heart-rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical to Gaussian noise, and both parts can be directly determined from the measured heart-rate data. Studies of 27 healthy subjects reveal that in most cases, the deterministic part has a form typically seen in bistable systems: there are two stable fixed points and one unstable one.

Cardiovascular System↗
PubMed2003

Translational and nontranslational motion of perturbed Turing patterns.

When the front and rear boundaries of a Turing pattern with nonzero flux boundary conditions move synchronously, several modes of motion of the pattern are found. Traveling boundaries can be obtained experimentally by illuminating a Turing-unstable system through a moving mask consisting of a single dark stripe with a light intensity sufficient to suppress pattern formation. All structured moving patterns belong to two general types: smooth translation at low mask velocity v(x) and nontranslational ("hopping") at intermediate v(x). At high v(x), Turing patterns are unable to form, and an unstructured striped image of the mask is seen. When the mask width exceeds the Turing wavelength, bistability between different types of moving patterns can occur as v(x) is varied.

Journal Article↗
PubMed2003

Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling.

Small lattices of N nearest-neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in an N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case N>2. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bistable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but nonsymmetric and phase shifted. For an intermediate range of time lags, inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.

Journal Article↗
PubMed2003

Signal detection via residence times statistics: noise-mediated minimization of the measurement error.

We study the problem of detecting a small dc signal by quantifying its effect on the mean difference DeltaT in residence times in the stable steady states of a bistable dynamical measurement device, in the presence of a noise floor and a known time-sinusoidal bias signal. Errors in the measurement process occur due to a finite observation time that is present in most practical scenarios. The error is found to have a nonmonotonic dependence on the noise intensity; at a critical noise intensity, the error is minimized. This phenomenon, reminiscent of the well-known stochastic resonance effect, can also be obtained by adjusting the device tuning parameters for a given noise floor. The effect appears to be most pronounced for subthreshold bias signals in the strongly nonlinear response regime.

Journal Article↗
PubMed2003

Low-frequency fluctuations in the Lang-Kobayashi equations.

The Lang-Kobayashi equations are simplified by a local analysis that focuses, in the long-delay-time limit, on one pair of mode-antimode only. In the domain of hysteresis between the two steady states, low frequency fluctuations (LFF) can be observed if there is a domain of bistability where both steady states are unstable. The high-frequency oscillations and the drop-offs in the LFF regime are associated with a dynamics close to the unstable upper and lower branch steady states, respectively.

Journal Article↗
PubMed2003

Subthreshold stochastic resonance: rectangular signals can cause anomalous large gains.

The main objective of this work is to explore aspects of stochastic resonance (SR) in noisy bistable, symmetric systems driven by subthreshold periodic rectangular external signals possessing a large duty cycle of unity. Using a precise numerical solution of the Langevin equation, we carry out a detailed analysis of the behavior of the first two cumulant averages, the correlation function, and its coherent and incoherent parts. We also depict the nonmonotonic behavior versus the noise strength of several SR quantifiers such as the average output amplitude, i.e., the spectral amplification, the signal-to-noise ratio, and the SR gain. In particular, we find that with subthreshold amplitudes and for an appropriate duration of the pulses of the driving force, the phenomenon of stochastic resonance is accompanied by SR gains exceeding unity. This analysis thus sheds light on the interplay between nonlinearity and the nonlinear response, which in turn yields nontrivial unexpected SR gains above unity.

Journal Article↗
PubMed2003

Comment on "Hysteresis phenomena in CO catalytic oxidation system in the presence of inhomogeneities of the catalyst surface".

Scrutinizing the Monte Carlo algorithm, used by D.-Y. Hua and Y.-Q. Ma [Phys. Rev. E 66, 066103 (2002)] in order to simulate the effect of defect sites on bistable kinetics of CO oxidation on single-crystal surfaces, we show that in their study (i) the rules for describing CO adsorption, desorption, and surface diffusion contradict the detailed balance principle and (ii) the ratio of the rates of CO diffusion and reaction between adsorbed CO and O species is opposite compared to that observed in reality.

Comment↗
PubMed2004

Propagating waves in one-dimensional discrete networks of coupled units.

We investigate the behavior of discrete systems on a one-dimensional lattice composed of localized units interacting with each other through nonlocal, nonlinear reactive dynamics. In the presence of second-order and third-order steps coupling two or three neighboring sites, respectively, we observe, for appropriate initial conditions, the propagation of waves which subsist in the absence of mass transfer by diffusion. For the case of the third-order (bistable) model, a counterintuitive effect is also observed, whereby the homogeneously less stable state invades the more stable one under certain conditions. In the limit of a continuous space the dynamics of these networks is described by a generic evolution equation, from which some analytical predictions can be extracted. The relevance of this mode of information transmission in spatially extended systems of interest in physical chemistry and biology is discussed.

Journal Article↗