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Periodic solutions of a periodic delay predator-prey system. (English) Zbl 0917.34057
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 $\omega$.

34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34K20Stability theory of functional-differential equations
34C25Periodic solutions of ODE
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