Vol. 13, no.3, 2021


Mathematical Foundations of the Fractal Scaling Method in Statistical Radiophysics and Applications

Alexander A. Potapov

Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, http://cplire.ru/
Moscow 125009, Russian Federation
Jinan University, Sino-Russian Laboratory of Information Technologies and fractal signal processing, https://english.jnu.edu.cn/
Guangzhou 510632, China
E-mail: potapov@cplire.ru

Received May 04, 2021, peer-reviewed May 24, 2021, accepted May 31, 2021

Abstract: The system of basic mathematical concepts and constructions underlying the modern global fractal-scaling method developed by the author is presented. An overview of the main results on the creation of new information technologies based on textures, fractals (multifractals), fractional operators, scaling effects and nonlinear dynamics methods obtained by the author and his students for more than 40 years (from 1979 to the present) at the Kotelnikov IRE of RAS. It is shown that, for the first time in the world, new dimensional and topological (and not energy!) features or invariants were proposed and then effectively applied for problems in radio physics and radio electronics, which are combined under the generalized concept of "sample topology" ~ "fractal signature". The author discovered, proposed and substantiated a new type and new method of modern radar, namely, fractal-scaling or scale-invariant radar (MIR). It should be noted that fractal radars are, in fact, a necessary intermediate stage on the path of transition to cognitive radar and quantum radar.

Keywords: fractal, scaling, fractional operator, texture, non-Markov random process, signature, nonlinear dynamics, radiophysics, radar

UDC 510.22: 517.2: 519.24: 537.86 + 621.396.96

RENSIT, 2021, 13(3):245-296 DOI: 10.17725/rensit.2021.13.245.

Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/399/13(3)245-296e.pdf