Fractal Manifold Method in Systems with Self-Organized Criticality

Complex nonlinear dynamic systems with a tendency to self-organization are considered herein. The article is aimed at obtaining a quantitative assessment of self-organization criticality in theoretical and practical aspects for computer calculations. The problem of direct processing of large arrays of non-Gaussian data is solved without the usual prior transformation into Gaussian data. The proposed method is relevant for situations when the cross-correlation of data in the array is significant, reflecting such processes as avalanches, chain reactions, and collective effects. In the simplest case of one-dimensional space, an algorithm is given for construction of a fractal manifold – a new mathematical object, the argument for which was proposed in [9]. The construction of the fractal manifold made it possible to reveal an unusual property of the Gauss function, which confirms the chosen approach. The fractal manifold method makes it possible to determine more accurately the average value due to its smaller scale in comparison to the Euclidean scale. The algorithm is invariant for linear transformations of the initial data set, has renormalization-group invariance, and determines the intensity of cross-correlation (self-organized criticality effect) of the data. The description of the self-organized criticality state is universal and does not depend on the nature of data correlation similar to the universality of the random variables’ distribution in the absence of data correlation. This method can be used with large sets of non-Gaussian or strange data obtained in information technology.

• Publication year

  2020

• Venue

  International Journal of Engineering Research and Technology

• Publication date

  2020-11-30

• Fields of study

  Physics, Computer Science

• Identifiers
  DOI 10.37624/IJERT/13.11.2020.3835-3839
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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