Oscillation analysis of \(\theta\)-methods for the Nicholson's blowflies model
The paper is concerned with discretizations of Nicholson's blowflies model NEWLINE\[NEWLINE N'(t)=-\delta N(t)+PN(t-\tau)e^{-aN(t-\tau)},\quad t\geq 0, NEWLINE\]NEWLINE w.r.t. oscillations arround the positive equilibrium NEWLINE\[NEWLINE N^\ast:=\frac{1}{a}\log\frac{P}{\delta}. NEWLINE\]NEWLINE Both for the linear \(\theta\)-method as well as for the one-leg \(\theta\)-method, the author derives various conditions under with the numerical solution oscillates. In addition, it is established that every non-oscillatory discretized solution tends to the equilibrium point \(N^\ast\). These results are illustrated using numerical simulations.
scientific article; zbMATH DE number 6574170