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Stability and Bifurcation for a Delayed Predator–Prey Model and the Effect of Diffusion

✍ Scribed by Teresa Faria

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
226 KB
Volume
254
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider a predator᎐prey system with one or two delays and a unique positive equilibrium E#. Its dynamics are studied in terms of the local stability of E# and of the description of the Hopf bifurcation that is proven to exist as one of Ž . the delays taken as a parameter crosses some critical values. We also consider a reaction᎐diffusion system with Neumann conditions, resulting from adding one spatial variable and diffusion terms in the previous model. The spectral and bifurcation analysis in the neighborhood of E#, now as a stationary point of this latter system, is addressed and the results obtained for the case without diffusion are applied. ᮊ 2001 Academic Press 1 4 stants. In the absence of predators, the prey species follows the logistic 1 Work partially supported under projects PRAXISrPCEXrPrMATr36r96 and PRAX-Ž . ISr2r2.1rMATr125r94 of FCT Portugal .

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