Dynamics of Moment Neuronal Networks with Intra- and Inter-Interactions

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