= Delayed logistic equation
{title2=$u'(t)=u(t)[1-u(t-\tau)]$}
This <delay differential equation> replaces instantaneous logistic inhibition by a population value one delay earlier. A positive <history function of a delay differential equation> gives positive solutions while they exist. The equilibria are zero and one. <Linearization> at one gives $x'(t)=-x(t-\tau)$, with characteristic equation $\lambda=-e^{-\lambda\tau}$. Delayed sign reversal permits overshoots around one and, at the <delayed logistic Hopf threshold>, a periodic branch.
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