  Directed complex network of two-state model neurons linked by synapses which
can be blocked or activated stochastically in time undergoes phase transition
between the quiescent phase with zero activity and the active one with
persistent activity. Avalanches of activity appear in the quiescent phase after
occasional excitation of randomly chosen neuron. Size and duration
distributions of long avalanches which we observe near phase transition point
are exponential. Only a small fraction of all neurons are active at any moment
of a long avalanche.
