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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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[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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