  In this study, we apply a mean field theory to the neural network model with
two periodic inputs in order to clarify the conditions of synchronies. This
mean field theory yields a self-consistent condition for the synchrony and
enables us to study the effects of synaptic connections for the behavior of
neural networks. Then, we have obtained a condition of synaptic connections for
the synchrony with the cycle time $T$. The neurons in neural networks receive
sensory inputs and top-down inputs from outside of the network. When the
network neurons receive two or more inputs, their synchronization depends on
the conditions of inputs. We have also analyzed this case using the mean field
theory. As a result, we clarified the following points: (1) The stronger
synaptic connections enhance the shorter synchrony cycle of neurons. (2) The
cycle of the synchrony becomes longer as the cycle of external inputs becomes
longer. (3) The relationships among synaptic weights, the properties of input
trains, and the cycle of synchrony are expressed by one equation, and there are
two areas for asynchrony. In association with the third point, the yielded
equation is so simple for calculation that they can easily provide us feasible
and infeasible conditions for synchrony.
