Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 254, Issue 2, Pages 433-463Publisher
ACADEMIC PRESS INC
DOI: 10.1006/jmaa.2000.7182
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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 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. (C) 2001 Academic Press.
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