相关论文: A Hamilton-Jacobi approach to characterize the evo…
We consider a population with two equal dominated species, dynamics of which is defined by one-dimensional piecewise-continuous, two parametric functions. It is shown that for any non-zero parameters this function has two fixed points and…
We analyze the long term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present extinction…
We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…
We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
The influence of migration on the stochastic dynamics of subdivided populations is still an open issue in various evolutionary models. We develop here a self-consistent mean-field-like method in order to determine the effects of migration…
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 provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy…
We study Hamilton-Jacobi equations in [0, +$\infty$) of evolution type with nonlinear boundary conditions of Neumann type in the case where the Hamiltonian is non necessarily convex with respect to the gradient variable. In this paper, we…
We present a new setting of the geometric Hamilton-Jacobi theory by using the so-called time-evolution operator K. This new approach unifies both the Lagrangian and the Hamiltonian formulation of the problem developed in a previous paper…
Biological organisms have to cope with stochastic variations in both the external environment and the internal population dynamics. Theoretical studies and laboratory experiments suggest that population diversification could be an effective…
The distributions of galaxy properties vary with environment, and are often multimodal, suggesting that the galaxy population may be a combination of multiple components. The behaviour of these components versus environment holds details…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
In subdivided populations, migration acts together with selection and genetic drift and determines their evolution. Building up on a recently proposed method, which hinges on the emergence of a time scale separation between local and global…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…
We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP…