  The deterministic dynamics of randomly connected neural networks are studied,
where a state of binary neurons evolves according to a discreet-time
synchronous update rule. We give a theoretical support that the overlap of
systems' states between the current and a previous time develops in time
according to a Markovian stochastic process in large networks. This Markovian
process predicts how often a network revisits one of previously visited states,
depending on the system size. The state concentration probability, i.e., the
probability that two distinct states co-evolve to the same state, is utilized
to analytically derive various characteristics that quantify attractors'
structure. The analytical predictions about the total number of attractors, the
typical cycle length, and the number of states belonging to all attractive
cycles match well with numerical simulations for relatively large system sizes.
