# Dynamics of a Prey-predator System with Foraging Facilitation in Predators

## TL;DR

This paper analyzes a prey-predator model with predator foraging facilitation, using advanced algebraic methods to determine equilibrium conditions and bifurcations, supported by numerical simulations.

## Contribution

It introduces a novel analytical approach combining pseudo-division and polynomial discrimination to study complex bifurcations in predator-prey dynamics.

## Key findings

- Identified parameter conditions for equilibria
- Classified bifurcation types including Hopf and Bogdanov-Takens
- Validated results with numerical simulations

## Abstract

The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root isolation technique and complete discrimination system of polynomial to obtain parameter conditions for the exact number of equilibria and their qualitative properties as well as a complete investigation of bifurcations including saddle-node, transcritical, pitchfork, Hopf and Bogdanov-Takens bifurcations. Moreover, numerical simulations are presented to support our theoretical results.