Stability of the logistic population model with delayed environmental response

The population dynamics model $\dfrac{dy}{dt} = \varepsilon y(t)\left( 1-\dfrac{1}{N} \sum\limits_{k=0}^{n}a_k y(t-\tau_k)\right)$, $\varepsilon>0$, $N>0$, $a_k\geqslant 0$, $\tau_k\geqslant 0$ $(0\leqslant k\leqslant n)$, $\sum\limits_{k=0}^{n} a_k=1$, was considered. For this model with uniform distribution of delays ($\tau_k=k\tau$, $\tau>0$) and $a_n=0$, nonnegativeness and convexity of the sequence $a_k$ $(0\leqslant k\leqslant n)$ $\sum\limits_{k=0}^{n}a_k \tau_k$. .