ABSTRACT
Mimimal models of coordinated behavior of populations living in the same environment are introduced for the cases when they either both gain by mutual interactions, or one hunts the other one, or finally when they compete with each other. 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 the competition case: tristability may be achieved showing that the principle of competitive exclusion fails in this case. Indeed either one of the competing populations may thrive, but also the case of populations coexistence is allowed, for the same set of parameter values.
