Periodicity in a Gause-type predation model considering collaboration among predators


  • Eduardo González Olivares Pontificia Universidad Católica de Valparaíso
  • Alejandro Rojas-Palma Departamento de Matemática, Física y Estadística, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca, Chile.



Predator-prey model, functional response, cooperation, stability, bifurcations, limit cycles


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.

Author Biography

Eduardo González Olivares, Pontificia Universidad Católica de Valparaíso

Profesor titular Jubilado


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How to Cite

González Olivares, E., & Rojas-Palma, A. (2021). Periodicity in a Gause-type predation model considering collaboration among predators. Selecciones Matemáticas, 8(02), 267-273.