相关论文: Global dynamics of a size-structured forest model

We continue to study (see arXiv:2401.08618, https://doi.org/10.48550/arXiv.2401.08618) a renewal equation $\phi(t)=\frak F\phi_t$ proposed in [C. Barril et al., J. Math. Biology, https://doi.org/10.1007/s00285-024-02084-x] to model trees…

Concerns about biodiversity and the long-term stability of forest ecosystems have lead to changing attitudes with respect to plantations. These artificial communities are ubiquitous, yet provide reduced habitat value in comparison to their…

We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational…

We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…

Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…

First, we systemize ealier results the uniform persistence for discrete model $A_{n+1}=A_nF(A_{n-m})$ of population growth, where $F:(0,\infty)\to(0,\infty)$ is continuous and strictly decreasing. Second, we investigation the effect of…

A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition.…

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 study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…

In this article we investigate the semiflow properties of a class of state-dependent delay differential equations which is motivated by some models describing the dynamics of the number of adult trees in forests. We investigate the…

In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this…

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…

We consider the general second order difference equation $x_{n+1}=F(x_n,x_{n-1})$ in which $F$ is continuous and of mixed monotonicity in its arguments. In equations with negative terms, a persistent set can be a proper subset of the…

We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n>=1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov…

We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…

In this paper, we investigated the global attractivity of the positive constant steady state solution of the mature population $w(t,x)$ governed by the age-structured model: \begin{equation*} \left\{\begin{array}{ll} \frac{\partial…

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…

We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…

We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the…