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Mathematical Problems in Engineering
Volume 2015, Article ID 381271, 13 pages
Research Article

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

1College of Mathematics and Computational Science, Hunan University of Arts and Science, Changde 415000, China
2Department of Mathematics, Hunan College of Finance and Economics, Changsha 410205, China

Received 6 July 2014; Accepted 7 September 2014

Academic Editor: Shifei Ding

Copyright © 2015 Xuyan Xiang and Jianguo Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.