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Fractal properties of percolation clusters in Euclidian neural networks

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  • Franović, Igor
  • Miljković, Vladimir

Abstract

The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools. Local population dynamics is characterized by three key parameters – probability for pool connectedness, synaptic strength and neuron refractoriness. The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing the critical parameter. Applying the finite-size scaling method, we infer a family of critical lines for various synaptic strengths and refractoriness values, and determine the Hausdorff–Besicovitch fractal dimension of the percolation clusters.

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  • Franović, Igor & Miljković, Vladimir, 2009. "Fractal properties of percolation clusters in Euclidian neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1418-1425.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1418-1425
    DOI: 10.1016/j.chaos.2007.06.026
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    References listed on IDEAS

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    1. Bai, Cheng-Lin & Zhao, Hong, 2007. "New types of interactions between solitary waves in (2+1)-dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 375-382.
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