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Zbl 1035.34084
Ruan, Shigui
Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays. (English)
[J] Q. Appl. Math. 59, No. 1, 159-173 (2001). ISSN 0033-569X; ISSN 1552-4485/e

The author investigates the asymptotic stability of equilibria in Kolmogorov-type predator-prey systems and gives criteria for absolute stability (stability independent of the delay), conditional stability (stability if the delay is not too large), and the occurence of Hopf bifurcations for critical delays. The method is based on the criterion in {\it J. K. Hale, E. F. Infante} and {\it F.-S. P. Tsen} [J. Math. Anal. Appl. 105, 533--555 (1985; Zbl 0569.34061)].
[Jan Sieber (Bristol)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
92D25 Population dynamics
34K18 Bifurcation theory of functional differential equations

Keywords: Kolmogorov-type predator-prey system; discrete delayed feedback

Citations: Zbl 0569.34061

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