  Objective: Brain is a fantastic organ that helps creature adapting to the
environment. Network is the most essential structure of brain, but the
capability of a simple network is still not very clear. In this study, we try
to expound some brain functions only by the network property. Methods: Every
network can be equivalent to a simplified network, which is expressed by an
equation set. The dynamic of the equation set can be described by some basic
equations, which is based on the mathematical derivation. Results (1) In a
closed network, the stability is based on the excitatory/inhibitory synapse
proportion. Spike probabilities in the assembly can meet the solution of a
nonlinear equation set. (2) Network activity can spontaneously evolve into a
certain distribution under different stimulation, which is closely related to
decision making. (3) Short memory can be formed by coupling of network
assemblies. Conclusion: The essential property of a network may contribute to
some important brain functions.
