The stability and Hopf bifurcation for a predator-prey system with discrete and distributed delays

In this paper, we investigate a predator-prey model with discrete and distributed delays. By choosing the discrete delay as a bifurcation parameter, we show that Hopf bifurcation occur as delay crosses a critical value. Then using normal form theorem and central manifold argument, we obtain the prop...

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Bibliographic Details
Main Authors: Zhiping Shu, Zuoliang Xiong, Zhifang He
Format: Conference Proceeding
Language:English
Subjects:
Asymptotic stability
Bifurcation
Delay
Delay effects
discrete and distributed delays
Hopf bifurcation
Numerical stability
periodic solution
Predator prey systems
predator-prey
stability
Stability analysis
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Summary:In this paper, we investigate a predator-prey model with discrete and distributed delays. By choosing the discrete delay as a bifurcation parameter, we show that Hopf bifurcation occur as delay crosses a critical value. Then using normal form theorem and central manifold argument, we obtain the property of the bifurcation periodic solution. Finally, we give an example to support our theoretical analysis.
ISSN:1948-2914
1948-2922
DOI:10.1109/BMEI.2010.5639236