Interacting population models with pack behavior

TL;DR

This paper introduces models of population interactions in shared environments, analyzing their equilibria and stability, revealing phenomena like coexistence, bifurcations, and tristability in competitive and symbiotic systems.

Contribution

It presents new mathematical models for population interactions, including the discovery of tristability in competitive scenarios, expanding understanding of ecological dynamics.

Findings

Coexistence can lead to global stability in symbiotic populations.

Hopf bifurcations occur in predator-prey models.

Tristability emerges in competitive interactions.

Abstract

Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The equilibria of the systems are analysed, showing that in some cases the populations may both disappear. Coexistence leads to global asymptotic stability for symbiotic populations, or to Hopf bifurcations for predator-prey systems. Finally, a new very interesting phenomenon is discovered in one of these rather simple models. Indeed tristability may be achieved in the competition case, for which competitive exclusion is allowed to occur together with populations coexistence.