Related papers: On decay-surge population models
These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
We study emergent dynamics of the discrete Cucker-Smale (in short, DCS) model with randomly switching network topologies. For this, we provide a sufficient framework leading to the stochastic flocking with probability one. Our sufficient…
Branching processes are models used to describe populations that reproduce and die over time. In the classical setting, an individual's reproductive capacity remains constant throughout its lifetime. However, in real-world situations,…
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
We consider scalar perturbations of energy--density for a class of cosmological models where an early phase of accelerated expansion evolves, without any fine--tuning for graceful exit, towards the standard Friedman eras of observed…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…
We study relations between the decaying rates of operator semigroups on Hilbert spaces and some spectral properties of their respective generators; in particular, we show that the decaying rates of orbits of semigroups which are stable but…
We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture,…
We show that the mean inverse populations of nondecreasing, square integrable, continuous-time branching processes decrease to zero like the inverse of their mean population if and only if the initial population $k$ is greater than a first…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including…