Search results for "moment equation"
showing 9 items of 9 documents
Increasing Neural Stem Cell Division Asymmetry and Quiescence Are Predicted to Contribute to the Age-Related Decline in Neurogenesis.
2018
Summary: Adult murine neural stem cells (NSCs) generate neurons in drastically declining numbers with age. How cellular dynamics sustain neurogenesis and how alterations with age may result in this decline are unresolved issues. We therefore clonally traced NSC lineages using confetti reporters in young and middle-aged adult mice. To understand the underlying mechanisms, we derived mathematical models that explain observed clonal cell type abundances. The best models consistently show self-renewal of transit-amplifying progenitors and rapid neuroblast cell cycle exit. In middle-aged mice, we identified an increased probability of asymmetric stem cell divisions at the expense of symmetric di…
Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization
2003
This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of…
The moment equation closure method revisited through the use of complex fractional moments
2015
In this paper the solution of the Fokker Planck (FPK) equation in terms of (complex) fractional moments is presented. It is shown that by using concepts coming from fractional calculus, complex Mellin transform and related ones the probability density function response of nonlinear systems may be written in discretized form in terms of complex fractional moment not requiring a closure scheme.
Statistic moments of the total energy of potential systems and application to equivalent non-linearization
2000
In this paper some properties of the total energy moments of potential systems, subjected to external white noise processes, are shown. Potential systems with a polynomial form of energy-dependent damping have been considered. It is shown that the analytical relations between the statistical moments of the energy associated with such systems can be obtained with the aid of the standard Ito calculus. Furthermore, it is shown that, for the stationary case, these analytical relations are very useful for the application of the equivalent non-linearization technique.
Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes
2008
This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Ito's stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, t…
Moment Equations for a Spatially Extended System of Two Competing Species
2005
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…
Stochastic dynamics and mean field approach in a system of three interacting species
2008
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on Lotka-Volterra equations. A correlated dichotomous noise acts on \beta, the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of each one of the three species. We study the time behaviour of the three species in single site for different values of the multiplicative noise intensity, finding noise-induced oscillations of the three species densities with an anticorrelated behaviour of the two preys. Afterwar…
Equivalent Non-Linearization of Hysteretic Systems by Means of RPS
2018
BackgroundThe analysis of elastoplastic systems with hardening (Bouc-Wen systems) under stochastic (seismic) loads needs the evaluation of higher order statistics even in the simplest case of normal distributed input. ObjectiveIn this paper, a non-linearization technique is proposed in order to evaluate the moments of any order of the response. MethodThis technique is developed by means of a nonlinear class of systems whose statistics are a priori known. The parameters of such systems can be chosen in such a way that the two systems are equivalent in a wide sense. Result & ConclusionIn the paper, the strategy to obtain the equivalence and the reliability of the results are discussed.
Dynamics of three interacting species in single compartment and in spatially extended system by moment equations
2008
Real ecosystems are influenced by random fluctuations of environmental parameters, such as temperature, food resources, migrations, genetic changes. This caused, during last decades, an increasing interest on the role played by the noise in population dynamics. In systems governed by nonlinear dynamics the presence of noise sources can give rise to counterintuitive phenomena like stochastic resonance, noise enhanced stability, resonant activation, noise delayed extinction. Therefore, the stability of biological systems in the presence of noise sources has become one of the most relevant topics both in experimental and theoretical investigations on complex systems. In this work we consider t…