Global well-posedness and stability analysis of prey-predator model with indirect prey-taxis

Abstract

This paper deals with a prey-predator model with indirect prey-taxis, which means chemical of prey causes the directional movement of the predator. We prove the global existence and uniform boundedness of solutions to the model for general functional responses in any spatial dimensions. Moreover, through linear stability analysis, it turns out that prey-taxis is an essential factor in generating pattern formations. This result differs in that the destabilizing effect of taxis does not occur in the direct prey-taxis case. In addition, we show the global stability of the semi-trivial steady state and coexistence steady state for some specific functional responses. We give numerical examples to support the analytic results. (C) 2019 Elsevier Inc. All rights reserved.