Related papers: Nonlinear Dynamics in Distributed Systems
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…
We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which…
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or…
In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
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…
A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally $\Phi$-entropies. Via purely analytic arguments it can be shown that these…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
The principal aim of the present work is to explore limit theorems for small random perturbations of a planar impulsive dynamical system, where impulses occur at hitting times of a suitable switching surface, and are thus state-dependent.…
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
An open stochastic system \`a la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeterminism caused by a fundamental lack of information. We…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…