Related papers: Dynamics of the Non-autonomous Owen-Smith Model
In recent years, Winter's nonlinear model has been adopted in theoretical physics as the prototype for the study of quantum resonances and the dynamics of observables in the context of nonlinear Schr\"odinger equations. However, its…
By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of particles over a shared resource guides the…
In this paper, we consider a non-autonomous allelopathic phytoplankton competition ODE model, incorporating the influence of fear effects observed in natural biological phenomena. Based on Mawhin's coincidence degree theory some sufficient…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
In this paper, the dynamics of a phytoplankton-zooplankton system with linear functional responses are examined. For the continuous-time model, the global asymptotic stability of the fixed points is demonstrated by constructing Lyapunov…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
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…
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We present and rigorously analyze a model describing a mixed…
We use a stochastic metapopulation model to study the combined effects of seasonality and spatial heterogeneity on disease persistence. We find a pronounced effect of enhanced persistence associated with strong heterogeneity, intermediate…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
A generalized seasonally-varying predator-prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the trophic…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…