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Ecological modeling and Lagrangian approach

Boris Arkhipov, Viacheslav Solbakov, Mikhail Solov’ev, Dmitry Shapochkin (2013)

Open Mathematics

A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...

Effects of competition and predation in a three species model

Janusz Szwabiński, Andrzej Pękalski, Kamil Trojan (2008)

Banach Center Publications

A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.

Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System

J.-C. Poggiale, M. Gauduchon, P. Auger (2008)

Mathematical Modelling of Natural Phenomena

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”...

Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses

Changjin Xu, Qianhong Zhang, Maoxin Liao (2013)

Applications of Mathematics

In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.

Extinction in nonautonomous Kolmogorov systems

Joanna Pętela (2010)

Applicationes Mathematicae

We consider nonautonomous competitive Kolmogorov systems, which are generalizations of the classical Lotka-Volterra competition model. Applying Ahmad and Lazer's definitions of lower and upper averages of a function, we give an average condition which guarantees that all but one of the species are driven to extinction.

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