<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the species affect each other through the limitation coefficients, rather then through the growth rates. This appears to be more realistic: the presence of foxes is not likely to diminish the fertility of rabbits, but will contribute to limiting rabbit's population. Both the cases of predation and of competition are considered, as well as competition in case of periodic coefficients. Our model becomes linear when one switches to the reciprocals of the variables. In another direction we use a similar idea to derive a multiplicity result for a class of periodic equations.</p>
</abstract>

In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the species affect each other through the limitation coefficients, rather then through the growth rates. This appears to be more realistic: the presence of foxes is not likely to diminish the fertility of rabbits, but will contribute to limiting rabbit's population. Both the cases of predation and of competition are considered, as well as competition in case of periodic coefficients. Our model becomes linear when one switches to the reciprocals of the variables. In another direction we use a similar idea to derive a multiplicity result for a class of periodic equations.

On the interaction of species capable of explosive growth

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"On the interaction of species capable of explosive growth"}

In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the...

On the interaction of species capable of explosive growth

Published Online: Feb 03, 2021

Page range: 401 - 410

Received: Sep 03, 2020

Accepted: Nov 05, 2020

DOI: https://doi.org/10.2478/amns.2021.1.00004

Keywords
Explosive growth, predator-prey, competing species

© 2021 Philip Korman, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

On the interaction of species capable of explosive growth

Published Online: Feb 03, 2021

Page range: 401 - 410

Received: Sep 03, 2020

Accepted: Nov 05, 2020

DOI: https://doi.org/10.2478/amns.2021.1.00004

KeywordsExplosive growth, predator-prey, competing species

© 2021 Philip Korman, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Keywords
Explosive growth, predator-prey, competing species