A framework of moment neuronal networks with intra- and inter-interactions is presented. It is to show how the spontaneous\nactivity is propagated across the homogeneous and heterogeneous network.The input-output firing relationship and the stability\nare first explored for a homogeneous network. For heterogeneous network without the constraint of the correlation coefficients\nbetween neurons, amore sophisticated dynamics is then explored.With random interactions, the network gets easily synchronized.\nHowever, desynchronization is produced by a lateral interaction such as Mexico hat function. It is the external intra layer input unit\nthat offers a more sophisticated and unexpected dynamics over the predecessors. Hence, the work further opens up the possibility\nof carrying out a stochastic computation in neuronal networks.
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