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Analytical Condition for Synchrony in a Neural Network with Two Periodic Inputs

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.