Related papers: A Stochastic Capital-Labour Model with Logistic Gr…
In this paper we investigate a stochastic model for an economic game. To describe this model we have used a Wiener process, as the noise has a stabilization effect. The dynamics are studied in terms of stochastic stability in the stationary…
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
How high should be the rate of immigration into a stochastic population in order to significantly reduce the probability of observing the population extinct? Is there any relation between the population size distributions with and without…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
A birth-death lattice gas model about the influence of an environment on the fitness and concentration evolution of economic entities is analytically examined. The model can be mapped onto a high order logistic map. The control parameter is…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic…
We give a criterion for unlimited growth with positive probability for a large class of multidimensional stochastic models. As a by-product, we recover the necessary and sufficient conditions for recurrence and transience for critical…
This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a…
The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…
Economic growth is unpredictable unless demand is quantified. We solve this problem by introducing the demand for unpaid spare time and a user quantity named human capacity. It organizes and amplifies spare time required for enjoying…
The well-known stochastic SIS model characterized by highly nonlinear in epidemiology has a unique positive solution taking values in a bounded domain with a series of dynamical behaviors. However, the approximation methods to maintain the…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Stochastic production planning problems were studied in several works; the model with one production good was discussed in [3]. The extension to several economic goods is not a trivial issue as one can see from the recent works [4], [5] and…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a…
Can cost-reducing technical change lead to a fall in the long run rate of profit if class struggle manages to keep the rate of exploitation constant? In a general circulating capital model, we derive sufficient conditions for cost-reducing…