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Zbl 0754.34078
Kulenović, M.R.S.; Ladas, G.; Sficas, Y.G.
Global attractivity in Nicholson's blowflies.
(English)
[J] Appl. Anal. 43, No.1-2, 109-124 (1992). ISSN 0003-6811; ISSN 1563-504X/e

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 $(e\sp{\delta\tau}-1)\left({p\over\delta}- 1\right)<1$. Then any solution $N(t)$ of (1) with $N(0)>0$ and $N(s)\ge 0$ for $s\in[-\tau,0]$ satisfies $\lim\sb{t\to+\infty}N(t)=N\sp*\equiv{1\over a}\ln\left({p\over\delta}\right)$.
[G.Karakostas (Ioannina)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
34K99 Functional-differential equations
92D25 Population dynamics

Keywords: global attractivity; asymptotic equilibrium; Nicholson's blowflies; delay differential equation

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