Displaying similar documents to “Extinction in nonautonomous Kolmogorov systems”

On the age-dependent predator-prey model

Antoni Leon Dawidowicz, Anna Poskrobko, Jerzy Leszek Zalasiński (2011)

Applicationes Mathematicae

Similarity:

The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.

Simulating Kinetic Processes in Time and Space on a Lattice

J. P. Gill, K. M. Shaw, B. L. Rountree, C. E. Kehl, H. J. Chiel (2011)

Mathematical Modelling of Natural Phenomena

Similarity:

We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown ...

Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space

Hiromi Seno (2010)

Mathematical Modelling of Natural Phenomena

Similarity:

With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the...

Effects of competition and predation in a three species model

Janusz Szwabiński, Andrzej Pękalski, Kamil Trojan (2008)

Banach Center Publications

Similarity:

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.

Lotka-Volterra type predator-prey models: Comparison of hidden and explicit resources with a transmissible disease in the predator species

Luciana Assis, Malay Banerjee, Moiseis Cecconello, Ezio Venturino (2018)

Applications of Mathematics

Similarity:

The paper deals with two mathematical models of predator-prey type where a transmissible disease spreads among the predator species only. The proposed models are analyzed and compared in order to assess the influence of hidden and explicit alternative resource for predator. The analysis shows boundedness as well as local stability and transcritical bifurcations for equilibria of systems. Numerical simulations support our theoretical analysis.

Spatial stochastic predator-prey models

Mauro Mobilia, Ivan T. Georgiev, Uwe C. Täuber (2008)

Banach Center Publications

Similarity:

We consider a broad class of stochastic lattice predator-prey models whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the deterministic rate equations, on the properties of the stochastic models. Here, we outline the robust scenario obeyed by most of the lattice predator-prey models with an interaction à la Lotka-Volterra. We also show how a drastically different behavior...