Related papers: Hierarchical size-structured populations: The line…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…
Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…
Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified…
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations…
A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is non-zero and/or its age structure is…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth"…
In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker's type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
In this paper we propose an existence and uniqueness theory for the solutions of a system of non-linear hyperbolic conservation laws, structured in age and maturity variables, representing a tissue environment. In particular we are…
This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…