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Effects of small-world connectivity on noise-induced temporal and spatial order in neural media

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  • Perc, Matjaž

Abstract

We present an overview of possible effects of small-world connectivity on noise-induced temporal and spatial order in a two-dimensional network of excitable neural media with FitzHugh–Nagumo local dynamics. Small-world networks are characterized by a given fraction of so-called long-range couplings or shortcut links that connect distant units of the system, while all other units are coupled in a diffusive-like manner. Interestingly, already a small fraction of these long-range couplings can have wide-ranging effects on the temporal as well as spatial noise-induced dynamics of the system. Here we present two main effects. First, we show that the temporal order, characterized by the autocorrelation of a firing-rate function, can be greatly enhanced by the introduction of small-world connectivity, whereby the effect increases with the increasing fraction of introduced shortcut links. Second, we show that the introduction of long-range couplings induces disorder of otherwise ordered, spiral-wave-like, noise-induced patterns that can be observed by exclusive diffusive connectivity of spatial units. Thereby, already a small fraction of shortcut links is sufficient to destroy coherent pattern formation in the media. Although the two results seem contradictive, we provide an explanation considering the inherent scale-free nature of small-world networks, which on one hand, facilitates signal transduction and thus temporal order in the system, whilst on the other hand, disrupts the internal spatial scale of the media thereby hindering the existence of coherent wave-like patterns. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed.

Suggested Citation

  • Perc, Matjaž, 2007. "Effects of small-world connectivity on noise-induced temporal and spatial order in neural media," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 280-291.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:2:p:280-291
    DOI: 10.1016/j.chaos.2005.10.018
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    1. S. Redner, 1998. "How popular is your paper? An empirical study of the citation distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 4(2), pages 131-134, July.
    2. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    3. Bernardo A. Huberman & Lada A. Adamic, 1999. "Growth dynamics of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 131-131, September.
    4. Kevin McCann & Alan Hastings & Gary R. Huxel, 1998. "Weak trophic interactions and the balance of nature," Nature, Nature, vol. 395(6704), pages 794-798, October.
    5. Per O. Seglen, 1992. "The skewness of science," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 43(9), pages 628-638, October.
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