Related papers: Populations facing a nonlinear environmental gradi…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
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…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of…
Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary…
We suggest a natural approach that leads to a modification of classical quasispecies models and incorporates the possibility of population extinction in addition to growth. The resulting modified models are called open. Their essential…
Chemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system of equations introduced by Keller and Segel has proven a popular choice in the modelling of such…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…
We investigate the long-time behavior of phenotype-structured models describing evolutionary dynamics of asexual populations, and analyze the joint effects of nonlocal interactions and spatial resource distributions on the global dynamics…
This paper explores a non-linear, non-local model describing the evolution of a single species. We investigate scenarios where the spatial domain is either an arbitrary bounded and open subset of the $n$-dimensional Euclidean space or a…
This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which…
Spatio-temporal pattern formation in complex systems presents rich nonlinear dynamics which leads to the emergence of periodic nonequilibrium structures. One of the most prominent equations for the theoretical and numerical study of the…
We study the asymptotic behavior of an integro-dierential equation describing the evolutionary adaptation of a population structured by a phenotypic trait. The model takes into account mutation, selection, horizontal gene transfer and…