Periodic solutions of a periodic delay predator-prey system

Yongkun, Li

doi:10.1090/S0002-9939-99-05210-7

Periodic solutions of a periodic delay predator-prey system
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Proc. Amer. Math. Soc. 127 (1999), 1331-1335 Request permission

Abstract:

The existence of a positive periodic solution for \begin{equation*} \begin {cases} \frac {\mathrm {d}H(t)}{\mathrm {d}t}=r(t)H(t) \left [1-\frac {H(t-\tau (t))}{K(t)}\right ] -\alpha (t)H(t) P(t),\ \frac {\mathrm {d}P(t)}{\mathrm {d}t}=-b(t)P(t)+\beta (t)P(t)H(t-\sigma (t)) \end{cases} \end{equation*} 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 $\omega$.

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