| Abstract: |
| We consider the fundamental non-autonomous linear scalar delay differential equation
$$ \dot{x}(t) = - a(t)x(t) + b(t)x(t-\tau) ,$$
with non-negative time-varying coefficients, representing the birth-death process of a population with maturation delay.
We review all previous results for this equation, then we prove a completely new asymptotic stability result
for the zero solution.
We construct a specific class of examples showing that our conditions for population extinction are
indeed complement all previous theorems in the literature. |
|