  Population dynamics in random ecological networks are investigated by
analyzing a simple deterministic equation. It is found that a sequence of
abrupt changes of populations punctuating quiescent states characterize the
long time behavior. An asymptotic analysis is developed by introducing a
log-scaled time, and it is shown that such a dynamical process behaves as
non-steady weak chaos in which population disturbances grow algebraically in
time. Also, some relevance of our study to taxonomic data of biological
extinction is mentioned.
