Global dynamics of Bazykin-type cross-diffusive model with indirect predator-taxis

This paper investigates the Bazykin-type cross-diffusive system which incorporates the prey-taxis with 'volume-filling' effect and the evasive defense with signaling mechanism in two-dimensional case. To compare with the fully cross-diffusive prey-predator model, this system exhibits two new features: The prey directly move towards to the opposite concentration gradient of the chemical signal which released by the predators, on the other hand, the predator engage competition interactions. Given suitably regular initial value, it is shown that this system admits a globally bounded classical solution without any restrictiveness on the parameters of the system. The current results supplement the conditions (Mishra and Wrzosek, JDE, 2023) which are used to prevent any blow-up of classical solution to this system. Moreover, we also prove that the prey-only steady state and coexistence steady state is globally convergent.