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Zbl 0869.34056
So, Joseph W.-H.; Yu, J.S.
Global attractivity and uniform persistence in Nicholson's blowflies.
(English)
[J] Differ. Equ. Dyn. Syst. 2, No.1, 11-18 (1994). ISSN 0971-3514; ISSN 0974-6870/e

Summary: The delay differential equation $$\dot N(t)= -\delta N(t)+ PN(t-\tau)e^{-aN(t-\tau)},\quad t\ge 0\tag{*}$$ was used by {\it W. S. C. Gurney}, {\it S. P. Blythe} and {\it R. M. Nisbet} [Nature 287, 17-21 (1980)] in describing the dynamics of Nicholson's blowflies. We show that for $P\le\delta$, every nonnegative solution of $(*)$ tends to zero as $t\to\infty$. On the other hand, for $P>\delta$, $(*)$ is uniformly persistent. Moreover, if in addition, $(e^{\delta r}- 1)\ln{P\over\delta}<1$, then every positive solution of $(*)$ tends to $N^*={1\over a}\ln {P\over \delta}$ as $t\to\infty$.
MSC 2000:
*34K99 Functional-differential equations
92D25 Population dynamics
92D40 Ecology

Keywords: delay differential equation; dynamics of Nicholson's blowflies; positive solution

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