Related papers: On population resilience to external perturbations
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
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…
Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
A large amount of population models use the concept of a carrying capacity. Simulated populations are bounded by invoking finite resources through a survival probability, commonly referred to as the Verhulst factor. The fact, however, that…
In this work, we provide an asymptotic analysis of the solutions to an elliptic integro-differential equation. This equation describes the evolutionary equilibria of a phenotypically structured population, subject to selection, mutation,…
The subject of this paper is inspired by \cite{CC} and \cite{CCP}. In \cite{CC} the authors investigate the dynamics of a population in a heterogeneous environment by means of diffusive logistic equations. An important part of their study…
This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
We consider birth and death stochastic dynamics of particle systems with attractive interaction. The heuristic generator of the dynamics has a constant birth rate and density dependent decreasing death rate. The corresponding statistical…
In this paper, we study two local--nonlocal settings for parabolic--elliptic evolution systems. In our problems we have a disjoint partition of the spacial domain $\Omega$ as $\Omega=A\cup B$ and we first consider a local parabolic equation…
We study the combined effects of periodically varying carrying capacity and survival rates on the fish population in the ocean (sea). We introduce the Getz type delay differential equation model with a control parameter which describes how…
This paper deals with some control problems related to structured population dynamics with diffusion. Firstly, we investigate the regional control for an optimal harvesting problem (the control acts in a subregion $\omega$ of the whole…
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations…
We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…
This paper concerns an age-structured juvenile-adult model with harvesting pulse and moving boundaries in a heterogeneous environment, in which the moving boundaries describe the natural expanding front of species and human periodic pulse…
The present paper is devoted to the study of the long term dynamics of diffusion processes modelling a single species that experiences both demographic and environmental stochasticity. In our setting, the long term dynamics of the diffusion…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We study population dynamics through a general growth/degrowth-fragmentation process, with resource consumption and unbounded growth/degrowth, birth and death rates. Our model is structured in a positive trait called energy (which is a…