Exploring unique dynamics in a predator-prey model with generalist predator and group defence in prey

TL;DR

This paper investigates a predator-prey model with a generalist predator and prey group defense, revealing finite-time blow-up and quenching phenomena, supported by numerical analysis and bifurcation studies.

Contribution

It introduces a novel finite-time blow-up and quenching concept in predator-prey dynamics with group defense and generalist predators, expanding current understanding.

Findings

Finite-time blow-up of predator populations.

Prey populations quench in finite time.

Rich bifurcation structures with multiple limit cycles.

Abstract

In the current manuscript, we consider a predator-prey model where the predator is modeled as a generalist using a modified Leslie-Gower scheme, and the prey exhibits group defence via a generalised response. We show that the model could exhibit finite time blow-up, contrary to the current literature (Eur. Phys. J. Plus 137, 28). We also propose a new concept via which the predator population blows up in finite time while the prey population quenches in finite time. The blow-up and quenching times are proved to be one and the same. Our analysis is complemented by numerical findings. This includes a numerical description of the basin of attraction for large data blow-up solutions, as well as several rich bifurcations leading to multiple limit cycles, both in co-dimension one and two. Lastly, we posit a delayed version of the model with globally existing solutions for any initial data.