Related papers: Stochastic description of delayed systems

We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…

We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…

In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…

Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…

Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…

This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…

Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent…

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein.…

We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

We introduce, and formally establish, a variant of the Hawkes-fed birth-death process -- the delayed Hawkes birth-death process -- in which the conditional intensity does not increase at arrivals but at departures from the system. In a…

This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…

Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…

Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…

We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation, instead it is based upon a dynamical…

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…