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- D. I. Iudin, Yaroslav D. Sergeyev, Masashi Hayakawa
- Applied Mathematics and Computation
- 2012

In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and… (More)

- D. I. Iudin, David B Gelashvili, Guillaume Rozenberg
- Doklady Biological Sciences
- 2003

Self-similarity is quite a common feature of natural systems: basins of large rivers, branched channels of lightning discharge, the spatial structure of microbial colonies, the patterns of star matter distribution in the space, and many other strongly nonequilibrium systems related in one way or another to the transfer of intense flows of matter, charge,… (More)

- David B Gelashvili, Andrey I. Dmitriev, D. I. Iudin, Guillaume Rozenberg, Leonid A Solntsev
- Doklady Biological Sciences
- 2008

257 The late Quaternary evolution of the Volga–Ural paleobiocenosis has been used as an example to demonstrate the possibility of applying multifractal analysis to the species structure of fossil small-mammal communities. No logical contradictions have been found between the ecological specificities of small-mammal communities, as considered in temporal… (More)

- David B Gelashvili, E V Cheprunov, D. I. Iudin
- Zhurnal obshcheĭ biologii
- 2004

We have proposed and validated a method for quantitative assessment of phenotypic diversity of natural populations. Method is based on the fluctuated asymmetry (FA) indices of bilateral organisms, and it is applicable for biondicative investigations. Convolution of functions was proposed to estimate the mean (population) value of FA complex of features.… (More)

- David B Gelashvili, D. I. Iudin, Guillaume Rozenberg
- Doklady Biological Sciences
- 2006

233 In our earlier studies [1, 2], we considered the application of multifractal formalism to the analysis of the species structure of biotic communities. Using macrozoobenthos of flatland lakes as an example, we demonstrated that the number of species found in samples ( S ) was a power function of the total number of these samples ( N ), which proved… (More)

- David B Gelashvili, D. I. Iudin, Guillaume Rozenberg, N V Iakimov
- Zhurnal obshcheĭ biologii
- 2007

Applications of the fractal to describing the species structure of communities are discussed. Fundamental notions of fractal geometry are explained in the first part. The problem of applying the concept of fractal to describe the spatial allocation of particular species and of community as a whole is reviewed in the second part. In the final part, the usage… (More)

- David B Gelashvili, D. I. Iudin, +7 authors M. S. Snegireva
- Biology Bulletin
- 2012

The principles and methods of fractal analysis of the species structure of freshwater phytoplankton, zooplankton, and macrozoobenthos communities of plain water reservoirs and urban waterbodies are discussed. The theoretical foundation and experimental verification are provided for the authors’ concept of self-similar (quasi-fractal) nature of the species… (More)

- David B Gelashvili, D. I. Iudin, +5 authors A. A. Kirillov
- Doklady Biological Sciences
- 2009

374 The species structure of biotic communities is an urgent and intensely debated problem of theoretical ecology, which attracts much attention of ecologists [1, 2]. Fractal analysis based on the idea of self-similarity is one of promising approaches to studying the structure of free-living organism communities [3–7]. However, the applicability of fractal… (More)

- Basil N Yakimov, D. I. Iudin, Leonid A Solntsev, David B Gelashvili
- Journal of theoretical biology
- 2014

The spatial structure of neutral communities has nontrivial properties, which are described traditionally by the Species-area relationship (SAR) and the Species Abundance Distribution, (SAD). Fractal analysis is an alternative way to describe community structure, the final product of which - a multifractal spectrum - combines information both on the scaling… (More)

- D. I. Iudin, V . Y . Trakhtengerts, Masao Hayakawa
- Physical review. E, Statistical, nonlinear, and…
- 2003

We have investigated the fractal dynamics of intracloud microdischarges responsible for the formation of a so-called drainage system of electric charge transport inside a cloud volume. Microdischarges are related to the nonlinear stage of multiflow instability development, which leads to the generation of a small-scale intracloud electric structure. The… (More)