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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.

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)
Full Text: DOI
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