Global Existence and Asymptotic Behavior in a Predator-Prey-Mutualist Model with Prey-Taxis

Abstract

This paper considers the global existence and boundedness of classical solutions to a predator-prey-mutualist model with prey-taxis. In addition, by constructing the Lyapunov functionals, we proved when $\alpha < (ac/b)·r +a/b,$ the positive equilibrium point is globally asymptotic stable; and when $\alpha \in ((ac/b)·r + a/b, M_1),$ the semi-trivial equilibrium point is globally asymptotic stable. Finally, we give some numerical examples to validate our results.