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Global attractivity in Nicholson’s blowflies. (English) Zbl 0754.34078
The paper deals with a delay differential equation of the form (1) $$\dot N(t)=-\delta N(t)+pN(t-\tau)\exp(-aN(t-\tau))$$ where $$\delta,p,a$$ and $$\tau$$ are positive real numbers and it is proved the following result: Assume $$p>\delta$$ and $$(e^{\delta\tau}-1)\left({p\over\delta}- 1\right)<1$$. Then any solution $$N(t)$$ of (1) with $$N(0)>0$$ and $$N(s)\geq 0$$ for $$s\in[-\tau,0]$$ satisfies $$\lim_{t\to+\infty}N(t)=N^*\equiv{1\over a}\ln\left({p\over\delta}\right)$$.

##### MSC:
 34K20 Stability theory of functional-differential equations 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 92D25 Population dynamics (general)
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##### References:
 [1] DOI: 10.1038/287017a0 · doi:10.1038/287017a0 [2] Kulenovic M.R.S., Bull. Math. Biol 49 pp 615– (1987) [3] DOI: 10.1007/BF01790539 · Zbl 0617.34071 · doi:10.1007/BF01790539
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