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Zbl 0917.34057
Li, Yongkun
Periodic solutions of a periodic delay predator-prey system. (English)
[J] Proc. Am. Math. Soc. 127, No.5, 1331-1335 (1999). ISSN 0002-9939; ISSN 1088-6826/e

Summary: The existence of a positive periodic solution for $$\align \frac{dH(t)}{dt}&= r(t)H(t) \left[1-\frac{H(t-\tau(t))}{K(t)}\right] -\alpha(t)H(t) P(t),\\ \frac{dP(t)}{dt}&= -b(t)P(t)+\beta(t)P(t)H(t-\sigma(t)), \endalign$$ is established, where $r$, $K$, $\alpha$, $b$, $\beta$ are positive periodic continuous functions with period $\omega>0$, and $\tau$, $\sigma$ are periodic continuous functions with period $\omega$.

MSC 2000:: *34K13 Periodic solutions of functional differential equations
92D25 Population dynamics
34K20 Stability theory of functional-differential equations
34C25 Periodic solutions of ODE

Keywords: delay equation; predator-prey system; periodic solution

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