Pursuit-evasion dynamics for Bazykin-type predator-prey model with indirect predator taxis

We study a pursuit-evasion diffusive predator-prey model which combines prey-taxis in predators with evasive defense strategy of prey being capable to move in the opposite direction to the gradient of a chem-ical signal secreted by the predators (indirect predator taxis). The kinetic part of the model extends the Rosenzweig MacArthur predator-prey model by assuming an intraspecific competition among predators, as in the classical Bazykin model. The prey-taxis takes into account density-dependent velocity suppression of predators while chasing the prey. The assumptions enable us to prove the existence of global-in-time clas-sical solutions for space dimension n <= 3 which are not expected to exist for the Rosenzweig MacArthur model according to numerical simulations which depict a finite time blow-up of solutions for n = 2.(c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

Automated summary

We studied a diffusive predator-prey model that incorporates prey-taxis and indirect predator taxis. This model extends the Rosenzweig MacArthur model by including intraspecific competition among predators. Our results showed the existence of global-in-time classical solutions for space dimension n <= 3, which is not expected in the Rosenzweig MacArthur model.