Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 36, pp. 1-14.

Title: Dynamics and pattern formation in diffusive
       predator-prey  models with predator-taxis

Authors: Zhongyuan Sun (Harbin Normal Univ., Harbin, Heilongjiang, China)
         Jinfeng Wang  (Harbin Normal Univ., Harbin, Heilongjiang, China)

Abstract:
 We consider a three-species predator-prey system in which the predator has a stage
 structure and the prey moves to avoid the mature predator, which is called the
 predator-taxis. We obtain the existence and uniform-in-time boundedness of 
 classical global  solutions for the model in any dimensional bounded domain 
 with the Neumann boundary  conditions. 
 If the attractive predator-taxis coefficient is under a critical value,
 the homogenerous positive steady state maintains its stability.
 Otherwise, the system may generate Hopf bifurcation solutions.
 Our results suggest that the predator-taxis amplifies the spatial heterogeneity of
 the three-species predator-prey system, which is different from the effect of that
 in two-species predator-prey systems.
 
Submitted December 25, 2019. Published  April 23, 2020.
Math Subject Classifications: 35K57, 35K59,  92D25
Key Words: Predator-prey; predator-taxis' global solution; spatial pattern.