  It is well known that a sparsely coded network in which the activity level is
extremely low has intriguing equilibrium properties. In the present work, we
study the dynamical properties of a neural network designed to store sparsely
coded sequential patterns rather than static ones. Applying the theory of
statistical neurodynamics, we derive the dynamical equations governing the
retrieval process which are described by some macroscopic order parameters such
as the overlap. It is found that our theory provides good predictions for the
storage capacity and the basin of attraction obtained through numerical
simulations. The results indicate that the nature of the basin of attraction
depends on the methods of activity control employed. Furthermore, it is found
that robustness against random synaptic dilution slightly deteriorates with the
degree of sparseness.
