Global existence and uniform boundedness in a diffusive food chain model with direct and indirect prey-taxis

In this paper, we propose a food chain model in which the primary predator moves directly toward areas of high prey density. Simultaneously, the primary predator, which serves as the prey for the secondary predator, indirectly influences the directional movements of the secondary predator through cues such as chemical signals, scents, or excretions. We investigate whether the distinct influences of direct taxis and indirect taxis, as observed in prey–predator dynamics, are also manifested in the proposed food chain model. Our study demonstrates that the model, which incorporates both direct and indirect prey-taxis, possesses bounded and global solutions up to three-dimensional space.