Ordering spatiotemporal chaos in discrete neural networks with small-world connectionsDu Qu Wei and Xiao Shu Luo
College of Physics and Electronic Engineering, Guangxi Normal University - Guilin 541004, China
received 14 January 2007; accepted in final form 8 May 2007; published June 2007
published online 1 June 2007
We investigate ordering of spatiotemporal chaos in two-dimensional map neuron (2DMN) networks with small-world (SW) connections, in which each neuron exhibits chaotic spiking-bursting behavior, focusing on the dependence of the spatiotemporal evolution on the topological randomness p. It is found that as the randomness p is increased, the chaotic spiking bursts become appreciably and more and more synchronized in space and coherent in time, and the maximal spatiotemporal order appears at a particular value of randomness p. However, if the randomness p is further increased, the temporal regularity is apparently destroyed, although spatial synchronization is enhanced. These phenomena imply that topological randomness can tame the spatiotemporal chaos in the 2DMN networks with SW connections. The comparison between this work and previous studies is made and it is found that the 2DMN network with small-world connections captures well the maximal spatiotemporal order. Our results may provide a useful tip for understanding the properties of collective dynamics in coupled real neurons.
87.18.Sn - Neural networks.
05.45.Xt - Synchronization; coupled oscillators.
89.75.Hc - Networks and genealogical trees.
© Europhysics Letters Association 2007