Global Stability in a Delayed Ratio-dependent Predator-prey System with Feedback Controls *

The aim of this paper is to study the dynamical behavior of solutions for a class of 3-species ratio-dependent predator-prey model with feedback controls and delays. Firstly, the attractivity of positive solutions for the system is discussed by using the Lyapunov stability theory. Secondly, some conditions are established to guarantee the globally asymptotic stability of the unique positive periodic solution for the corresponding periodic system by constructing a suitable Poincare mapping and using the fixed point theory. Finally, some numerical simulations are provided to verify the results obtained in this paper.