### A simple Gause-type predator-prey model considering social predation

**Keywords:**
stability, bifurcation, functional response, predator-prey model, limit cycle

### Abstract

The consumer-resource relationships are among the most fundamental of all ecological relationships and have been the focus of ecology since its beginnings. Usually are described by nonlinear differential equation systems, putting the emphasis in the effect of antipredator behavior (APB) by the prey; nevertheless, a minor quantity of articles has considered the social behavior of predators. In this work, two predator-prey models derived from the Volterra model are analyzed, in which the equation of predators is modified considering cooperation or collaboration among predators. It is well known that competition among predators produces a stabilizing effect on system describing the model, since there exists a wide set in the parameter space where the system has a unique equilibrium point in the phase plane, which is globally asymptotically stable. Meanwhile, the cooperation can originate more complex and unusual dynamics. As we will show, it is possible to prove that for certain subset of parameter values the predator population sizes tend to infinite when the prey population goes to extinct. This apparently contradicts the idea of a realistic model, when it is implicitly assumed that the predators are specialist, ie, the prey is its unique source of food. However, this could be a desirable effect when the prey constitutes a plague. To reinforce the analytical result, numerical simulations are presented.

### Más información

Título según WOS: | A simple Gause-type predator-prey model considering social predation |

Título de la Revista: | MATHEMATICAL METHODS IN THE APPLIED SCIENCES |

Volumen: | 42 |

Número: | 17 |

Editorial: | Wiley |

Fecha de publicación: | 2019 |

Página de inicio: | 5668 |

Página final: | 5686 |

Idioma: | English |

DOI: |
10.1002/mma.5372 |

Notas: | ISI |