Editorial
Effects of small spatial variation of the reproduction rate in a two species competition model.
Ein dauerhaftes Zusammenleben zweier Populationen.
Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System
This paper is devoted to the study of a predator-prey model in a patchy environment. The model represents the interactions between phytoplankton and zooplankton in the water column. Two patches are considered with respect to light availability: one patch is associated to the surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low enough to avoid ”paradox-enrichment”...
Équations d'évolution dégénérées
Equazione stocastica di dinamica di popolazioni di tipo preda-predatore
Si considera l'equazione stocastica che modellizza la dinamica di popolazioni di due specie di tipo preda-predatore sotto perturbazioni stocastiche. Si dimostrano in primo luogo l'esistenza e l'unicità della soluzione dell'equazione; per questo è essenziale introdurre una funzione ausiliaria con cui si costruiscono soluzioni approssimate. Si dimostra inoltre che, se non sono presenti perturbazioni stocastiche dovute alla stocasticità demografica, ma solo perturbazioni stocastiche rappresentanti...
Equilibrium transitions in finite populations of players
We discuss stochastic dynamics of finite populations of individuals playing symmetric games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of two-player games with two symmetric Nash equilibria, when the number of players increases, the population undergoes multiple transitions between its equilibria.
Estimates of solutions of impulsive parabolic equations and applications to the population dynamics.
A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.
Evolution in a changing environment: existence of solutions
We establish the existence of solutions of an intrinsically nonlinear differential-integral equation that arises from the mathematical modelling of the evolution of an asexual population in a changing environment. The main objective is to pave the way for a rigorous analysis of the linear stability of travelling wave solutions of the corresponding problem.
Evolution in a migrating population model
We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation , where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t)...
Existence and global asymptotical stability of periodic solution for the -periodic logistic system with time-varying generating operators and -periodic impulsive perturbations on Banach spaces.
Existence and global attractivity of periodic solutions in a higher order difference equation
Consider the following higher order difference equation where and are continuous functions in and periodic functions in with period , and is a nonnegative integer. We show the existence of a periodic solution under certain conditions, and then establish a sufficient condition for to be a global attractor of all nonnegative solutions of the equation. Applications to Riccati difference equation and some other difference equations derived from mathematical biology are also given.
Existence and global attractivity of periodic solutions in -species food-chain system with time delays.
Existence and global attractivity of positive almost periodic solutions for a kind of fishing model with pure-delay
By using some analytical techniques, modified inequalities and Mawhin's continuation theorem of coincidence degree theory, some sufficient conditions for the existence of at least one positive almost periodic solution of a kind of fishing model with delay are obtained. Further, the global attractivity of the positive almost periodic solution of this model is also considered. Finally, three examples are given to illustrate the main results of this paper.
Existence and global attractivity positive periodic solutions for a discrete model.
Existence and global stability of positive periodic solutions of a discrete predator-prey system with delays.
Existence and global stability of positive periodic solutions of a discrete delay competition system.
Existence and stability of periodic solutions for a nonlocal evolution population problem.
The theory of maximal monotone operators is applied to prove the existence of weak periodic solutions for a nonlinear nonlocal problem. The stability of these solutions is a consequence of the Lipschitz continuous assumption on the diffusivity matrix and the death rate.
Existence and uniqueness for the predator-prey model with diffusion in the scalar case.
We solve the problem of the existence and uniqueness of coexistence states for the classical predator-prey model of Lotka-Volterra with diffusion in the scalar case.
Existence and uniqueness of a positive steady state solution for a logistic system of differential difference equations.