Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay
A predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/252437 |
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| Summary: | A predator-prey system with disease in the predator is investigated, where the
discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local
analysis and Hopf bifurcation analysis. By analyzing the associated characteristic
equation, it is found that Hopf bifurcation occurs when τ crosses some critical values.
Using the normal form theory and center manifold argument, the explicit formulae
which determine the stability, direction, and other properties of bifurcating periodic
solutions are derived. |
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| ISSN: | 1026-0226 1607-887X |