Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls
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 s...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/186539 |
| 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. |
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| ISSN: | 1026-0226 1607-887X |