Topological probability and connection strength induced activity in complex neural networks

doi:10.1088/1674-1056/19/10/100513

Abstract Recent experimental evidence suggests that some brain activities can be assigned to small-world networks. In this work, we investigate how the topological probability p and connection strength C affect the activities of discrete neural networks with small-world (SW) connections. Network elements are described by two-dimensional map neurons (2DMNs) with the values of parameters at which no activity occurs. It is found that when the value of p is smaller or larger, there are no active neurons in the network, no matter what the value of connection strength is; for a given appropriate connection strength, there is an intermediate range of topological probability where the activity of 2DMN network is induced and enhanced. On the other hand, for a given intermediate topological probability level, there exists an optimal value of connection strength such that the frequency of activity reaches its maximum. The possible mechanism behind the action of topological probability and connection strength is addressed based on the bifurcation method. Furthermore, the effects of noise and transmission delay on the activity of neural network are also studied.

Keywords: topological probability small world connections connection strength neural networks activity

Received: 26 February 2010
Revised: 13 May 2010
Accepted manuscript online:

PACS:	02.50.Cw	(Probability theory)
	07.05.Mh	(Neural networks, fuzzy logic, artificial intelligence)

Fund: Project supported by the Key Program of National Natural Science Foundation of China (Grant No. 50937001), the National Natural Science Foundation of China (Grant Nos. 50877028, 10947011 and 10862001), the High Technology Research and Development Program of China (Grant No. 2007AA05Z229), the Science Foundation of Guangdong Province, China (Grant No. 8251064101000014), and the Construction of Key Laboratories in Universities of Guangxi Province, China (Grant No. 200912).

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Wei Du-Qu(韦笃取), Zhang Bo(张波), Qiu Dong-Yuan(丘东元), and Luo Xiao-Shu(罗晓曙) Topological probability and connection strength induced activity in complex neural networks 2010 Chin. Phys. B 19 100513

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