Boundedness and global stability of a diffusive prey–predator model with prey-taxis

A diffusive prey–predator model with prey-taxis and trophic interactions of three levels is proposed and analyzed, in which the predator could move in the direction of prey gradient. We prove the global existence and boundedness of solutions of the system on bounded domains with no-flux boundary condition. The result holds for arbitrary spatial dimension and any prey-taxis sensitivity coefficient. Moreover, we also prove that such prey-taxis does not qualitatively affect the existence and stability of nonnegative equilibria under some conditions.