Predator-prey models with competition, Part III: Classification of stationary solutions

TL;DR

This paper classifies stationary solutions in predator-prey models with multiple predator groups, showing conditions under which only constant solutions exist based on the number of groups and competition strength.

Contribution

It provides a complete characterization of positive solutions in multi-group predator-prey systems, highlighting the impact of group number and competition intensity.

Findings

Large number of predator groups leads to only constant solutions.

Weak competition results in only constant solutions.

Complete classification of solutions under specified conditions.

Abstract

For a stationary system representing prey and $N$ groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if the number of components $N$ is too large or if the competition between different groups is too small, then the system has only constant solutions, which we then completely characterize.