Related papers: A Mean Field Approximation of the Bolker-Pacala Po…
We extend our earlier mean field approximation of the Bolker-Pacala model of population dynamics by dividing the population into N classes, using a mean field approximation for each class but also allowing migration between classes as well…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
We consider a discrete model that describes a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize this model by adding…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
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,…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
We consider the extinction regime in the spatial stochastic logistic model in $\mathbb{R}^d$ (a.k.a. Bolker--Pacala--Dieckmann--Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space…
Markov Population Model is a commonly used framework to describe stochastic systems. Their exact analysis is unfeasible in most cases because of the state space explosion. Approximations are usually sought, often with the goal of reducing…
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 study Markov population processes on large graphs, with the local state transition rates of a single vertex being linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
Many complex systems can be described by population models, in which a pool of agents interacts and produces complex collective behaviours. We consider the problem of verifying formal properties of the underlying mathematical representation…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
We study the Bolker-Pacala-Dieckmann-Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space, and compete with each other…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results…
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired…
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with…