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 chemical 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 classical 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.