On the interaction of species capable of explosive growth

TL;DR

This paper introduces a novel population interaction model where species influence each other through limitation coefficients rather than growth rates, offering a more realistic perspective on predator-prey and competitive dynamics.

Contribution

It proposes an alternative to classical models by focusing on limitation coefficients, and explores both predation and competition, including periodic coefficient cases.

Findings

Model becomes linear with reciprocal variables.

Derived multiplicity results for periodic equations.

Provides a more realistic interaction framework.

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.