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Oscillation and global attractivity in a periodic Nicholson’s blowflies model. (English) Zbl 1012.34067
Here, the authors consider the following nonlinear delay differential equation $N'(t)=-\delta N(t)+P(t)N(t-m\omega)e^{-\alpha N(t-n\omega)},\tag{*}$ where $$m$$ is a positive integer, $$\delta(t)$$ and $$P(t)$$ are positive $$\omega$$-periodic functions. In the non-delay case, they show that equation (*) has a unique positive periodic solution and provide sufficient conditions for their global attractivity. In the delay case, they provide sufficient conditions for the oscillation of all positive solutions.

MSC:
 34K11 Oscillation theory of functional-differential equations 34K20 Stability theory of functional-differential equations 34K60 Qualitative investigation and simulation of models involving functional-differential equations 92D25 Population dynamics (general)
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