相关论文: Immigration-extinction dynamics of stochastic popu…

We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…

The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death and migration. Here we consider a Markov model of a population front propagating…

Host-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving…

We investigate stochastic extinction in an epidemic model and the impact of random vaccinations in large populations formulated in terms of an optimal escape path. We find that different random vaccination strategies can have widely…

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

Populations are often subject to catastrophes that cause mass removal of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the results reported, it has been considered whether dispersion…

We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…

The extinction of a single species due to demographic stochasticity is analyzed. The discrete nature of the individual agents and the Poissonian noise related to the birth-death processes result in local extinction of a metastable…

I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…

A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…

An ecological system with multiple stable equilibria is prone to undergo catastrophic change or regime shift from one steady-state to another. It should be noted that, if one of the steady states is an extinction state, the catastrophic…

This paper analyzes the stationary distributions of populations governed by the discrete stochastic logistic and Ricker difference equations at equilibrium examines with the gamma distribution. We identify mathematical relationships between…

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…

I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…

The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…

In this study, we analyze the relationship between human population growth and economic dynamics. To do so, we present a modified version of the Verhulst model and the Solow model, which together simulate population dynamics and the role of…

The objective of this article is to create a framework to study asymptotic equilibria in human populations with a special focus on immigration. We present a new model, based on Resource Dependent Branching Processes, which is now broad…

Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…