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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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