Search results for "stochastic process."

Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response.

2006

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena …

Gaussian models for the distribution of Brownian particles in tilted periodic potentials

2011

We present two Gaussian approximations for the time-dependent probability density function (PDF) of an overdamped Brownian particle moving in a tilted periodic potential. We assume high potential barriers in comparison with the noise intensity. The accuracy of the proposed approximated expressions for the time-dependent PDF is checked with numerical simulations of the Langevin dynamics. We found a quite good agreement between theoretical and numerical results at all times.

A numerical recipe for the computation of stationary stochastic processes' autocorrelation function

2023

Many natural phenomena exhibit a stochastic nature that one attempts at modeling by using stochastic processes of different types. In this context, often one is interested in investigating the memory properties of the natural phenomenon at hand. This is usually accomplished by computing the autocorrelation function of the numerical series describing the considered phenomenon. Often, especially when considering real world data, the autocorrelation function must be computed starting from a single numerical series: i.e. with a time-average approach. Hereafter, we will propose a novel way of evaluating the time-average autocorrelation function, based on the preliminary evaluation of the quantit…

Analysis of the human a-wave ERG component

2006

The a-wave is one of the main issues of research in the field of ocular electrophysiology, since it is strictly connected with early photoreceptoral activities. The present study proposes mathematical methods that analyse this component in human subjects, and supports experimental evidence relating to possible correlations among the responses of photoreceptoral units under a light stimulus. The investigation is organized in two parts: the first part concerns the onset and the initial slope, up to the first minimum (about 10-15 ms), the second part deals with the main portion of the wave, up to about 30 ms. In both cases, the a-waves, recorded at various levels of luminance, have been fitted…

Finite-time boundedness for uncertain discrete neural networks with time-delays and Markovian jumps

2014

This paper is concerned with stochastic finite-time boundedness analysis for a class of uncertain discrete-time neural networks with Markovian jump parameters and time-delays. The concepts of stochastic finite-time stability and stochastic finite-time boundedness are first given for neural networks. Then, applying the Lyapunov approach and the linear matrix inequality technique, sufficient criteria on stochastic finite-time boundedness are provided for the class of nominal or uncertain discrete-time neural networks with Markovian jump parameters and time-delays. It is shown that the derived conditions are characterized in terms of the solution to these linear matrix inequalities. Finally, n…

Stability analysis for stochastic hybrid systems: A survey

2014

This survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We re-emphasize the common features found in most of the models that have appeared in the literature, which include stochastic switched systems, Markov jump systems, impulsive stochastic systems, switching diffusions, stochastic impulsive systems driven by renewal processes, diffusions driven by Lévy processes, piecewise-deterministic Markov processes, general stochastic hybrid systems, and stochastic hybrid inclusions. Then we review many of the stability concepts that have been studied, inclu…

2014

This paper deals with the fault detection problem for a class of discrete-time wireless networked control systems described by switching topology with uncertainties and disturbances. System states of each individual node are affected not only by its own measurements, but also by other nodes’ measurements according to a certain network topology. As the topology of system can be switched in a stochastic way, we aim to designH∞fault detection observers for nodes in the dynamic time-delay systems. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are acquired to guarantee the existence of the filters satisfying theH∞performance constraint, and observer gains…

Stability analysis and controller design for a class of T-S fuzzy Markov jump system with uncertain expectation of packet dropouts

2013

This paper is concerned with an H∞ control for a class of Takagi-Sugeno (T-S) fuzzy Markov jump system under unreliable communication links. It is assumed that the transition probabilities determining the dynamical behavior of the underlying system are partially unknown and the communication links between the plant and the controller are imperfect (the packet dropouts occur intermittently). In this paper, a more practical scenario is considered in the setting, i.e., the expectation of packet losses represented as a description of Bernoulli-distributed stochastic process is uncertain. Attention is focused on the design of H∞ controllers such that the closed-loop system is stochastically stab…

Coupled stochastic dynamics of magnetic moment and anisotropy axis of a magnetic nanoparticle

2012

An algorithm is developed for numerical simulation of coupled stochastic dynamics of magnetic moment and magnetic anisotropy axis of a nanoparticle. Time-correlation functions of the magnetic moment and its components longitudinal and transverse to the magnetic anisotropy axis are calculated by averaging along the stochastic trajectory. The longitudinal and transverse relaxation times are found by fitting the time correlation functions. Existing theoretical relations derived by the effective field approach in the limit of small fields are confirmed. The time-correlation functions of magnetic moments of nanoparticles in dependence on their properties are calculated numerically for arbitrary …

Structure of rat behavior in hole-board: I) multivariate analysis of response to anxiety

2008

Aim of present paper was to carry out an analysis of rat behavior in hole-board following different multivariate approaches. Thirty male Wistar rats were observed in a hole-board apparatus and their behavior recorded for 10 min through a digital videocamera for a following frame-by-frame analysis. Both descriptive and multivariate analyses were used. Descriptive analysis showed that roughly 85% of the whole behavioral structure encompassed six patterns appearing during the first minute of observation: walking, climbing, rearing, immobile-sniffing, edge-sniff and head-dip. As to multivariate approach, cluster analysis showed three main dyadic associations: [edge-sniff/head-dip], [walking/cli…