Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays. (English) Zbl 1035.34084

Ruan, Shigui

Q. Appl. Math. 59, No. 1, 159-173 (2001).

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 J. K. Hale, E. F. Infante and F.-S. P. Tsen [J. Math. Anal. Appl. 105, 533–555 (1985; Zbl 0569.34061)].

Reviewer: Jan Sieber (Bristol)

MSC:

34K20	Stability theory of functional-differential equations
92D25	Population dynamics (general)
34K18	Bifurcation theory of functional-differential equations

Keywords:

Kolmogorov-type predator-prey system; discrete delayed feedback

Citations:

Zbl 0569.34061