Biomedical subjects

A R Bulsara

Publications and source records attributed to A R Bulsara.

12 recordsLinked to original sources

PubMed2004

Noisy FitzHugh-Nagumo model: from single elements to globally coupled networks.

We study the noisy FitzHugh-Nagumo model, representative of the dynamics of excitable neural elements, and derive a Fokker-Planck equation for both a single element and for a network of globally coupled elements. We introduce an efficient way to numerically solve this Fokker-Planck equation, especially for large noise levels. We show that, contrary to the single element, the network can undergo a Hopf bifurcation as the coupling strength is increased. Furthermore, we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency. This resonance is also investigated analytically by exploiting the different time scales in the problem.

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

Asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime: switching time distributions.

A detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented. The results are valid for any two-state system, however, the specific case of the Duffing potential is considered in detail. The dynamics are considered in the weak noise limit, i.e., when the response of the system to the external periodic field is strongly nonlinear. The system asymmetry is created by a nonzero dc component of the external force, and manifests itself as an asymmetry between the mean switching times between the potential wells. We obtain explicit analytic expressions for the whole hierarchy of switching time distributions (including the residence time and return time distributions). We also obtain expressions for the average residence times and describe how they depend on asymmetry, together with an explicit expression for the difference between the residence times in the weak noise limit; the results are presented in the context of using the switching dynamics to detect weak dc target signals.

Journal Article↗

PubMed2003

Signal detection via residence-time asymmetry in noisy bistable devices.

We introduce a dynamical readout description for a wide class of nonlinear dynamic sensors operating in a noisy environment. The presence of weak unknown signals is assessed via the monitoring of the residence time in the metastable attractors of the system, in the presence of a known, usually time-periodic, bias signal. This operational scenario can mitigate the effects of sensor noise, providing a greatly simplified readout scheme, as well as significantly reduced processing procedures. Such devices can also show a wide variety of interesting dynamical features. This scheme for quantifying the response of a nonlinear dynamic device has been implemented in experiments involving a simple laboratory version of a fluxgate magnetometer. We present the results of the experiments and demonstrate that they match the theoretical predictions reasonably well.

Journal Article↗

PubMed2003

Cooperative dynamics in a class of coupled two-dimensional oscillators.

We study a system of globally coupled two-dimensional nonlinear oscillators [using the two-junction superconducting quantum interference device (SQUID) as a prototype for a single element] each of which can undergo a saddle-node bifurcation characterized by the disappearance of the stable minima in its potential energy function. This transition from fixed point solutions to spontaneous oscillations is controlled by external bias parameters, including the coupling coefficient. For the deterministic case, an extension of a center-manifold reduction, carried out earlier for the single oscillator, yields an oscillation frequency that depends on the coupling; the frequency decreases with coupling strength and/or the number of oscillators. In the presence of noise, a mean-field description leads to a nonlinear Fokker-Planck equation for the system which is investigated for experimentally realistic noise levels. Furthermore, we apply a weak external time-sinusoidal probe signal to each oscillator and use the resulting (classical) resonance to determine the underlying frequency of the noisy system. This leads to an explanation of earlier experimental results as well as the possibility of designing a more sensitive SQUID-based detection system.

Journal Article↗

PubMed2002

Noise activated nonlinear dynamic sensors.

We introduce a novel dynamical description for a wide class of nonlinear physical sensors operating in a noisy environment. The presence of unknown physical signals is assessed via the monitoring of the residence times in the metastable attractors of the system. We show that the presence of ambient noise, far from degrading the sensor operation, can actually improve its sensitivity and provide a greatly simplified readout scheme, as well as significantly reduce processing procedures for this new class of devices that we propose to call noise activated nonlinear dynamic sensors. Such devices can also show interesting dynamical features such as the resonant trapping effect.

Journal Article↗

PubMed2001

Stochastic dynamics in a two-dimensional oscillator near a saddle-node bifurcation.

We study the oscillator equations describing a particular class of nonlinear amplifier, exemplified in this work by a two-junction superconducting quantum interference device. This class of dynamic system is described by a potential energy function that can admit minima (corresponding to stable solutions of the dynamic equations), or "running states" wherein the system is biased so that the potential minima disappear and the solutions display spontaneous oscillations. Just beyond the onset of the spontaneous oscillations, the system is known to show significantly enhanced sensitivity to very weak magnetic signals. The global phase space structure allows us to apply a center manifold technique to approximate analytically the oscillatory behavior just past the (saddle-node) bifurcation and compute the oscillation period, which obeys standard scaling laws. In this regime, the dynamics can be represented by an "integrate-fire" model drawn from the computational neuroscience repertoire; in fact, we obtain an "interspike interval" probability density function and an associated power spectral density (computed via Renewal theory) that agree very well with the results obtained via numerical simulations. Notably, driving the system with one or more time sinusoids produces a noise-lowering injection locking effect and/or heterodyning.

Journal Article↗

PubMed2001

Monostable array-enhanced stochastic resonance.

We present a simple nonlinear system that exhibits multiple distinct stochastic resonances. By adjusting the noise and coupling of an array of underdamped, monostable oscillators, we modify the array's natural frequencies so that the spectral response of a typical oscillator in an array of N oscillators exhibits N-1 different stochastic resonances. Such families of resonances may elucidate and facilitate a variety of noise-mediated cooperative phenomena, such as noise-enhanced propagation, in a broad class of similar nonlinear systems.

Journal Article↗

PubMed2001

Noninvasive control of stochastic resonance.

External feedback can enhance (or depress) the response of a noisy bistable system to monochromatic signals, significantly magnifying its natural stochastic resonance. We compare and contrast a variety of such feedback strategies, using both numerical simulations and analog electronic experiments. These noninvasive control techniques are especially valuable for noisy bistable systems that are difficult or impossible to modify internally.

Journal Article↗

PubMed2000

General measures for signal-noise separation in nonlinear dynamical systems.

We propose the straight phi divergences from statistics and information theory (IT) as a set of separation indices between signal and noise in stochastic nonlinear dynamical systems (SNDS). The straight phi divergences provide a more informative alternative to the signal-to-noise ratio (SNR) and have the advantage of being applicable to virtually any kind of stochastic system. Moreover, straight phi divergences are intimately connected to various fundamental limits in IT. Using the properties of straight phi divergences, we show that the classical stochastic resonance (SR) curve can be interpreted as the performance of a nonoptimal, or mismatched, detector applied to the output of a SNDS. Indeed, for a prototype double-well system with forcing in the form of white Gaussian noise plus a possible embedded signal, the whole information loss can be attributed to this mismatch; an optimal detection procedure (for the signal) gives the same performance when based on the output as when based on the input of the system. More generally, it follows that, when characterizing signal-noise separation (or system performance) of SNDS in terms of criteria that do not correspond to IT limits, the choice of criterion can be crucial. The indicated figure of merit will then not be universal and will be relevant only to some family of applications, such as the classical (narrow-band SNR) SR criterion, which is relevant for narrow-band post processing. We illustrate the theory using simple SNDS excited by both wide- and narrow-band signals; however, we stress that the results are applicable to a much larger class of signals and systems.

Journal Article↗

PubMed1997

First passage statistics of periodically driven models for neural dynamics.

The dynamics of two simple neuron models subjected to periodic stimuli is studied at the level of the first passage time probability density. The results from analytic treatments of these models are presented, and a discussion of the important properties displayed by these models is given. Specifically, both models possess resonans phenomena in the first passage probability distribution, arising from of the interplay of characteristic time-scales in the system.

Models, Biological↗

PubMed1989

Noise effects in an electronic model of a single neuron.

We consider a simple electronic circuit model of a single neuron. The neuron is assumed to be driven by an external signal comprising constant (dc) and random components. In addition, the nonlinearity parameter in the circuit is assumed to fluctuate, thereby giving rise to critical behavior including the onset of hysteresis phenomena even for system parameter values that would not otherwise support such behavior. This "noise-induced critical behavior" is analysed, in the long time limit, through a study of the probability density function describing the neural response.

Animals↗