abstr14

Assume that  zero is a stable equilibrium of
an ODE  x'   = f(x, p)  for parameter values  p < p0.
and becomes unstable for p > p0.
If we suppose that   p(t) varies slowly with t, then, under some
conditions, the trajectories of the nonautonomous ODE  x'(t)  = f(x(t),p(t)) 
stay close to zero even long after p(t)  has crossed the value p0.
This phenomenon is called `delayed loss of stability' and   is well-known  for ODEs.
In this paper, we  describe an analogous phenomenon for delay equations of the form  
x'(t) = f(t, x(t-1))$. We study an example which requires to combine linearization at zero
with estimates on the nonlinear behavior away from zero, and  where we  obtain an explicit
estimate on the time until the growth of  |x(t)|   becomes `visible'.


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