We study the long time behaviour of the transient before the collapse on the
periodic attractors of a discrete deterministic asymmetric neural networks
model. The system has a finite number of possible states so it is not possible
to use the term chaos in the usual sense of sensitive dependence on the initial
condition. Nevertheless, at varying the asymmetry parameter, k, one observes
a transition from ordered motion (i.e. short transients and short periods on
the attractors) to a ``complex'' temporal behaviour. This transition takes
place for the same value kc at which one has a change for the mean
transient length from a power law in the size of the system (N) to an
exponential law in N. The ``complex'' behaviour during the transient shows
strong analogies with the chaotic behaviour: decay of temporal correlations,
positive Shannon entropy, non-constant Renyi entropies of different orders.
Moreover the transition is very similar to that one for the intermittent
transition in chaotic systems: scaling law for the Shannon entropy and strong
fluctuations of the ``effective Shannon entropy'' along the transient, for k>kc.Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included