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Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls. (English) Zbl 1161.39020

Summary: A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator species \(y\) will be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.

MSC:

39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
93B52 Feedback control
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