Predators-prey models with competition Part I: existence, bifurcation and qualitative properties

TL;DR

This paper analyzes a predator-prey model incorporating competition, exploring solution existence, bifurcations, and asymptotic behaviors, revealing complex population dynamics and optimal configurations under varying conditions.

Contribution

It introduces a mathematical framework for predator competition in prey environments, studying solution properties, bifurcations, and optimal population distributions, including multiple competing groups.

Findings

Solutions exhibit different behaviors depending on parameters.

Existence of heterogeneous stationary solutions.

Optimal predator populations can include multiple competing groups.

Abstract

We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their asymptotic properties in time, showing that the solutions have different behavior depending on the choice of the parameters. We also construct heterogeneous stationary solutions and study the limits of strong competition and abundant resources. We then use these information to study some properties such as the existence of solutions that maximize the total population of predators. We prove that in some regimes the optimal solution for the size of the total population contains two or more groups of competing predators.