Related papers: Stochastic modelling of nonlinear dynamical system…
Two examples for the interplay between chaotic dynamics and stochastic forces within hydrodynamical systems are considered. The first case concerns the relaxation to equilibrium of a concentration field subject to both chaotic advection and…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition…
In this paper, we study the stationary states of diffusive dynamics driven out of equilibrium by reservoirs. For a small forcing, the system remains close to equilibrium and the large deviation functional of the density can be computed…