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Dynamics of a one-dimensional neural network with a “small world”—topology of synaptic connections

✍ Scribed by A Grabowski; R.A Kosiński; A Krawiecki

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
752 KB
Volume
341
Category
Article
ISSN
0378-4371

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✦ Synopsis

Dynamics of a one-dimensional neural network with external periodic stimulation are investigated numerically. Synaptic connections with constant and random values were assumed. Three ranges of network dynamics-periodic, intermediate and chaotic-were found, depending on the number of short-range synaptic connections k and the gain parameter g, which are the control parameters. The in uence of the number of k and additional r long-range connections (shortcuts), typical for a "small-world" network, on the dynamics of the system is discussed. With an increase in the values of g and k, clusters of neurons which do not follow external stimulation appear in the network. For large enough values of g and k, a network has chaotic dynamics. The presence of shortcuts may have either a stabilizing or destabilizing e ect on the dynamics of a network. In particular, the presence of shortcuts with certain locations may increase the susceptibility of network to external stimulation.

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