# Bifurcation analysis of a prey-predator model with predator intra-specific interactions and ratio-dependent functional response

## TL;DR

This paper analyzes a predator-prey model with predator intraspecific interactions and ratio-dependent response, revealing complex bifurcation behaviors and the effects of parameter changes on system stability.

## Contribution

It provides a detailed bifurcation analysis of the Bazykin predator-prey model with novel insights into stability and dynamics.

## Key findings

- Existence and stability of two interior equilibrium points.
- Identification of multiple bifurcation types including saddle-node, Hopf, homoclinic, and Bogdanov-Takens.
- Numerical simulations showing the impact of predator consumption rate and efficiency on system dynamics.

## Abstract

We study the Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response and show the existence and stability of two interior equilibrium points. We prove that the model displays a wide range of different bifurcations, such as saddle-node bifurcations, Hopf bifurcations, homoclinic bifurcations and Bogdanov-Takens bifurcations. We use numerical simulations to further illustrate the impact changing the predator per capita consumption rate has on the basin of attraction of the stable equilibrium points, as well as the impact of changing the efficiency with which predators convert consumed prey into new predators.