Boundedness and stabilization of a predator-prey model with attraction- repulsion taxis in all dimensions

Abstract

This paper establishes the existence of globally bounded classical solutions to a predator-prey model with attraction-repulsion taxis in a smooth bounded domain of any dimensions with Neumann boundary conditions. Moreover, the global stabilization of solutions with convergence rates to constant steady states is obtained. Using the local time integrability of the $ L^2 $-norm of solutions, we build up the basic energy estimates and derive the global boundedness of solutions by the Moser iteration. The global stability of constant steady states is established based on the Lyapunov functional method.

Keywords

• predator-prey
• attraction-repulsion
• global boundedness
• global stability