Related papers: From stochastic individual-based models to free-bo…

This article deals with the emergence of a specific mating preference pattern called homogamy in a population. Individuals are characterized by their genotype at two haploid loci, and the population dynamics is modelled by a non-linear…

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…

We extend the work on optimal investment and consumption of a population considered in [2] to a general stochastic setting over a finite time horizon. We incorporate the Cobb-Douglas production function in the capital dynamics while the…

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is…

We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…

Stochastic fluctuations are central to the understanding of extinction dynamics. In the context of population models they allow for the description of the transition from the vicinity of a non-trivial fixed point of the deterministic…

In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…

Growth models with internal habit formation have been studied in various settings under the assumption of deterministic dynamics. The purpose of this paper is to explore a stochastic version of the model in Carroll et al. [1997, 2000], one…

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…

Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…

We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…

Hamilton variational principle for special type of statistical ensemble of deterministic dynamical systems is derived. Thie form of variational principle allows one to describe the statistical ensemble in terms of wave functions and…

We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…

We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin)…

Dynamics among central sources (hubs) providing a resource and large number of components enjoying and contributing to this resource describes many real life situations. Modeling, controlling, and balancing this dynamics is a general…

In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…

This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but non-predicable parameter process, in addition to the…

Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approaches: deterministic models are computationally efficient but…