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

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