Periodicidad en modelos de depredación del tipo Gause considerando colaboración entre los depredadores

Abstract

Predation models are a great source of study from both an ecological and a mathematical point of view, especially for the analysis of trophic chains. The determination of the dynamics of the systems that describe them, as well as the verification of the nature of these properties by the interacting species, is a topic that is sometimes not always correlated. It is widely known that the incorporation of some mathematical descriptions of ecological phenomena strongly modifies the properties of many of these models. This implies that the systems describing such models are structurally unstable. In this work, we include collaboration or cooperation between predators, a social behavior that describes the help made to capture their favorite prey. It is described by a power function with an exponent between 0 and 1, to indicate the possible interference between them, despite their collaboration. The exponent is interpreted as the density-dependent aggregation index. We show that this assumption originates a varied behavior of the system, with respect to the associated Kolmogorov-type quadratic polynomial system that does not consider collaboration, including the existence of a stable limit cycle around a positive equilibrium point, among other analytical properties.