Periodic solutions of single-species models with periodic delay. (English) Zbl 0764.92016

Freedman, H. I.; Wu, Jianhong

SIAM J. Math. Anal. 23, No. 3, 689-701 (1992).

The authors consider several single-species population growth models with time delays, where both the coefficients (net birth rate, reproduction rate and self-inhibition rate) and the delays are periodic functions. It is shown that if the self-inhibition rate is sufficiently large compared to the reproduction rate, then the model equation has a globally asymptotically stable positive periodic solution.

Reviewer: A.I.Csetényi (Budapest)

MSC:

92D25	Population dynamics (general)
34K20	Stability theory of functional-differential equations
92D40	Ecology
34K25	Asymptotic theory of functional-differential equations

Keywords:

oscillations; delay equations; fixed point theorems; net birth rate; single-species population growth models; time delays; reproduction rate; self-inhibition rate; globally asymptotically stable positive periodic solution