Related papers: Large fluctuations in stochastic population dynami…
A change in a stochastic system has three representations: Probabilistic, statistical, and informational: (i) is based on random variable $u(\omega)\to\tilde{u}(\omega)$; this induces (ii) the probability distributions $F_u(x)\to…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
In two-strategy decision-making problems, individuals often imitate the highest earners or choose either the common or rare strategy. Individuals who benefit from the common strategy are conformists, whereas those who profit by choosing the…
We build upon the recent steady-state Penna model solution, Phys.Rev.Lett. 89, 288103 (2002), to study the population dynamics within the Penna model. We show, that any perturbation to the population can be broken into a collection of modes…
An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic…
This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…
We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…