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 α < ( ac / b ) · r + a / b , the positive equilibrium point is globally asymptotic stable; and when α ∈ (( ac / b ) · r + a / b , M 1 ) , the semi-trivial equilibrium point is globally asymptotic stable. Finally, we give some numerical exam-ples to validate our results.