Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

摘要

A ratio-dependent predator-prey system with Holling type III functional response and feedbackcontrols is proposed. By constructing a suitable Lyapunov function and using the comparisontheorem of difference equation, sufficient conditions which ensure the permanence and globalattractivity of the system are obtained. After that, under some suitable conditions, we show that thepredator species y will be driven to extinction. Examples together with their numerical simulationsshow that the main results are verifiable.