ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Potapov A. A. The origin and formation of fractal radiophysics and fractal radio electronics at the IRE RAS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 5, pp. 748-776. DOI: 10.18500/0869-6632-003183, EDN: YYRUFM

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon and_2025-5_potapov_748-776.pdf
(downloads: 0)
Full text PDF(En):
PDF icon and_2025_5_potapov_en.pdf
(downloads: 4)
Language: 
Russian
Heading: 
Science for Education. Methodical Papers. History.
Article type: 
Review
UDC: 
537.86 + 621.3
DOI: 
10.18500/0869-6632-003183
EDN: 
YYRUFM

The origin and formation of fractal radiophysics and fractal radio electronics at the IRE RAS

Autors: 
Potapov Alexander Alekseevich, Kotel'nikov Institute of Radioengineering and Electronics of Russian Academy of Sciences
Abstract: 

Purpose. The article describes the main points of the origin, formation and development of the application of fractal theory, topology, fractional dimension theory and scaling in solving problems of radio electronics and radiophysics in the USSR and Russia in the IRE of the USSR Academy of Sciences and IRE RAS, since the 80s of the XX century.

Methods.The relevance of the author’s research is related to the need for a more accurate description of the real processes occurring in modern intelligent radio systems. First of all, this takes into account the hereditarity (memory), non-Gaussianity, scaling (self-similarity, self-similarity) and topology of physical signals and fields.

Results. All research is carried out in the fundamental scientific direction "Fractal Radiophysics and Fractal Radioelectronics: Design of Fractal Radio Systems initiated and developed by the author at the V.A. Kotelnikov IRE RAS from 1979 to the present.

Conclusion. The author develops and reinforces his ideas that a new “fractal” dimension should be firmly introduced into radiosciences, and not as an auxiliary role, but as a fundamental explanatory factor. This allows us to move to a new level of the information structure of real nonMarkov signals and fields. The important role of RAS academician Yuri Vasilyevich Gulyaev in the development of this fundamental scientific field is shown. His participation is expressed, in particular, in his diverse assistance to the author in promoting his ideas in the USSR, Russia and the world.
 

Key words: 
fractal
texture
scaling
fractional derivatives
radio physics
radio electronics
multi-profile radio
Acknowledgments: 
This work was carried out within the framework of the State assignment of IRE RAS,theme “Ether – 3”.
Reference: 
  1. Potapov AA. Fractals in Radio Physics and Radar. .: Logos; 2002. 664 p. (in Russian).
  2. Potapov AA. Fractals in Radio Physics and Radar: Topology of a Sample. .: Universitetskaya kniga; 2005. 848 p. (in Russian).
  3. Potapov AA. Fractals and chaos as the basis for new breakthrough technologies in modern radio systems. In: Crownover RM. Fractals and Chaos in Dynamic Systems. .: Tekhnosphera; 2006. P. 374–479 (in Russian).
  4. Potapov AA, Gulyaev YuV, Nikitov SA, Pakhomov AA, German VA. The Latest Methods of Image Processing. .: Fizmatlit; 2008. 496 p. (in Russian).
  5. Gulyaev YuV, editor. Professor Alexander Alekseevich Potapov. Fractals in Action: Biography and Publication Index. M.: Raduga; 2019. 256 p. (in Russian).
  6. Gulyaev YV, Potapov AA. Application of fractal theory, fractional operators, textures, scaling effects, and nonlinear dynamics methods in the synthesis of new information technologies in radio electronics (specifically, radiolocation). J. Commun. Technol. Electron. 2019:64(9);911–925. DOI: 10.1134/S1064226919080059.
  7. Mandelbrot B. Les objects fractal forme, hasard et dimension. Paris: Flammarion; 1975. 190 p.
  8. Mandelbrot B. The Fractal Geometry of Nature. New York: W. H. Freeman; 1982. 468 p.
  9. Sokolov AV, editor. Issues of Advanced Radar. .: Radiotekhnika; 2003. 512 p. (in Russian).
  10.  Potapov AA, Wu Hao, Xiong Shan. Fractality of Wave Fields and Processes in Radar and Control. Guangzhou: South China University of Technology Press; 2020. 280 p.
  11.  Pavel’ev VA, Potapov AA. Influence of the ground surface on the structure of a pulse signal in millimeter wavelength band. J. Commun. Technol. Electron. 1994;39(4):573–582. (in Russian).
  12.  Potapov AA. Generalized correlator of fields scattered by rough surfaces. J. Commun. Technol. Electron. 1996;41(9):759–766. (in Russian).
  13.  Potapov AA, German VA. Detection of artificial objects with fractal signatures. Pattern Recognition and Image Analysis. 1998;8(2):226–229.
  14.  Potapov AA, German VA. Processing of optic and radar images of the earth surface by fractal methods. J. Commun. Technol. Electron. 2000;45(8):853–860.
  15.  Potapov AA. Fractals in radiophysics and radar. Elements of the theory of fractals: A review. J. Commun. Technol. Electron. 2000;45(11):1157–1164.
  16.  Opalenov YuV, Potapov AA. Application of stochastic signals and the radon transform to the formation of raster radar images by a microwave digital radar with fractal data processing. J. Commun. Technol. Electron. 2000;12:1311–1322.
  17.  Potapov AA. Fractal in radio physics and radio location: Fractal analysis of signals. J. Commun. Technol. Electron. 2001;46(3):237–246.
  18.  Potapov AA. Fractal in radio physics and radar: Fundamental theory of wave scattering by a fractal surface. J. Commun. Technol. Electron. 2002;47(5):461–487.
  19.  Potapov AA, German VA. Effects of deterministic chaos and strange attractor in the radar of dynamic systems of the vegetative cover type. Tech. Phys. Lett. 2002;28(7):586–588. DOI: 10.1134/ 1.1498793.
  20.  Potapov AA. New information technology in radar detection of low-contrast targets based on probabilistic texture and fractal features. J. Commun. Technol. Electron. 2003;48(9):1012–1029.
  21.  Potapov AA and German VA. Methods of measuring the fractal dimension and fractal signatures of a multidimensional stochastic signal. J. Commun. Technol. Electron. 2004;(12):1370–1391.
  22.  Potapov AA, Bulavkin VV, German VA, Vyacheslavova OF. Fractal signature methods for profiling of processed surfaces. Tech. Phys. 2005;75(5):560–575. DOI: 10.1134/1.1927210.
  23.  Potapov AA, German VA. Fractal processing of faint signals and low-contrast images. Optoelectron. Instrument. Proc. 2006;42(5):4–20.
  24.  Potapov AA. The theory of functionals of stochastic backscattering fields. J. Commun. Technol. Electron. 2007;52(3):245–292. DOI: 10.1134/S1064226907030011.
  25.  Potapov AA, Laktyunkin AV. Theory of the Wave Scattering by Anisotropic Fractal Surface. Journal Nonlinear World. 2008;6(1):3–36 (in Russian).
  26.  Potapov AA, Matveev EN. Fractal electrodynamics. Scaling of the fractal antennas based on ring structures and multiscale frequency–selective 3D media and fractal sandwiches: Transition to fractal nanostructures. J. Commun. Technol. Electron. 2010;55(10):1083–1101. DOI: 10.1134/ S1064226910100013.
  27.  Potapov AA. Fractal model and methods based on scaling in fundamental and applied problems of modern physics. In: Gorelik VS, Morozov AN, editors. Irreversible Processes in Nature and Technique. M.: Bauman Moscow State Tech. Univ. Publishing; 2007. Iss. II. P. 5–107 (in Russian).
  28.  Potapov AA. Fractals, scaling and fractional operators in information processing (Moscow Scientific School of Fractal Methods at the V. A. Kotelnikov Institute of Radio Electronics, Russian Academy of Sciences, 1981–2011). In: Gorelik VS, Morozov AN, editors. Irreversible Processes in Nature and Technique. M.: Bauman Moscow State Tech. Univ. Publishing; 2012. Iss. IV. P. 5–117. (in Russian).
  29.  Leonov KN, Potapov AA, Ushakov PA. Application of invariant properties of chaotic signals in the synthesis of noise-immune broadband systems for data transmission. J. Commun. Technol. Electron. 2014;59(12):1393–1411. DOI: 10.1134/S1064226914120110.
  30.  Potapov AA, Laktyun’kin A.V. Frequency coherence function of a space–time radar channel forming images of an anisotropic fractal surface and fractal objects. J. Commun. Technol. Electron. 2015;60(9):962–969. DOI: 10.1134/S1064226915090089.
  31.  Potapov AA, Il’yin ., Chigin P. Dimensional and topological effects in fractal-scaling detection and processing of many-dimensional signals. Bulletin of the Siberian State University of Telecommunications and Information Science. 2015;(2):51–66 (in Russian).
  32.  Potapov AA. On the strategic directions in synthesis of new types of radar textural-fractal detectors of low-contrast objects with marking off its outlines and coordinates against the background of high-intensity noise from the ground, sea and precipitations. In: Proc. IV All-Russian Scientific and Technical Conf. «RTI VKO Systems – 2016». 02–03 June 2016, Moscow, Russia. .: Bauman Moscow State Tech. Univ. Publishing; 2017. P. 438–448 (in Russian).
  33.  Potapov AA. Textural and fractal-scaling methods of detection, processing and identification of weak radar signals and soft images in the background of high-intensity noises. Bulletin of Aerospace Defense. 2018;2(18):15–26 (in Russian).
  34.  Potapov AA. Waves in large disordered fractal systems: Radar, nanosystems, and clusters of unmanned aerial vehicles and small-size spacecrafts. J. Commun. Technol. Electron. 2018;63(9): 980–997. DOI: 10.1134/S1064226918090176.
  35.  Bagmanov VKh, Potapov AA, Sultanov AKh, Zang W. Fractal filters intended for signal detection during remote-sensing data processing. J. Commun. Technol. Electron. 2018;63(10):1163–1169. DOI: 10.1134/S1064226918100030.
  36.  Potapov AA. On the dimension and non-linear dynamics theory application in a new form and method of radio location. Journal of Oceanological Research. 2019;47(1):100–102 (in Russian). DOI: 10.29006/1564-2291.JOR-2019.47(1).30.
  37.  Potapov AA. Fractal electrodynamics: Numerical modeling of small fractal antenna devices and fractal 3D microwave resonators for modern ultra-wideband or multiband radio systems. J. Commun. Technol. Electron. 2019;64(7):629–663. DOI: 10.1134/S1064226919060068.
  38.  Akinshin NS, Potapov AA, Bystrov RP, Esikov OV, Chernyshkov AI. Building systems for object recognition by multichannel sensing systems based on neural networks and fractal signatures. J. Commun. Technol. Electron. 2020;65(7):835–842. DOI: 10.1134/S1064226920060017.
  39.  Potapov AA, Kuznetsov VA, Pototskii AN. New class of topological textural multifractal descriptors and their application for processing low-contrast radar and optical images. J. Commun. Technol. Electron. 2021;66(5):581–590. DOI: 10.1134/S1064226921050090.
  40.  Potapov AA, Kuznetsov VA, Alikulov EA. Methods for complexing images formed by multi-band synthetic aperture radars. Journal of the Russian Universities. Radioelectronics. 2021;24(3):6–21 (in Russian). DOI: 10.32603/1993-8985-2021-24-3-6-21.
  41.  Potapov AA, Kuznetsov VA, Alikulov EA. Structural-parametric synthesis of systems for optimal texture-fractal processing of multidimensional radar images. J. Commun. Technol. Electron. 2022;67(1):63–78. DOI: 10.1134/S1064226922010077.
  42.  Akinshin NS, Potapov AA, Minakov EI, Timoshenko AV, Perlov AYu. Methods for evaluating the performance of a computer complex for monitoring the technical condition of radar stations and sensor platforms. J. Commun. Technol. Electron. 2022;67(5):567–572. DOI: 10.1134/ S1064226922050011.
  43.  Potapov AA, Kuznetsov VA. Textural-fractal analysis of polarimetric images generated by synthetic aperture radar. J. Commun. Technol. Electron. 2023;68(10):1127–1139. DOI: 10.1134/ S1064226923100145.
  44.  Podosenov SA, Potapov AA, Foukzon Ja, Men’kova ER. Nonholonomic, Fractal and Coupled Structures in Relativistic Continuous Media, Electrodynamics, Quantum Mechanics and Cosmology. .: URSS; 2015. 1128 p. (in Russian).
  45.  Blakhman AB, editor. Radar. Theory and Practice. Moscow: UNITY-DANA; 2023. 719 p. (in Russian).
  46.  Gulyaev YuV, Nikitov SA, Potapov AA, Davydov AG. Design of fractal radio systems: Numerical analysis of electromagnetic properties of the sierpinski fractal antenna. J. Commun. Technol. Electron. 2005;50(9):1070–1076 (in Russian).
  47.  Gulyaev YuV, Nikitov SA, Potapov AA, German VA. Concepts of scaling and fractal dimension in the design of a fractal detector of radio signals. J. Commun. Technol. Electron. 2006;51(8): 909–916. DOI: 10.1134/S1064226906080079.
  48.  Potapov AA. Waves, orbital angular momentum, bound states in the continuum, fractals and metasurfaces: Multi-profile radio. RENSIT: Radioelectronics. Nanosystems. Information Technologies. 2024;16(8):961–1008. DOI: 10.17725/j.rensit.2024.16.961.
  49.  Potapov AA. Multi-profile radio, fractal engineering, artificial intelligence and smart radio environments: A new approach based on the topology of fractal sets and intelligent meta surfaces. Evolutions Mech. Eng. 2025;5(5):EME.000623. DOI: 10.31031/EME.2025.05.000623.
  50.  Potapov AA, Kuznetsov VA, Goncharov SA. A simulation model for signature formation of complex low-observable targets. J. Commun. Technol. Electron. 2025;70(6):564–582 (in Russian).
  51.  Potapov AA, Tupik VA, Margolin VI, Kostrin DK. Ion-Plasma Formation of Nanosized Coatings with Fractal Topology. IJIE: Int. Journal of Integrated Engineering. 2024;16(9):284–293. DOI: 10.30880/ijie.2024.16.09.023.
  52.  Kuznetsov VA. Historical aspects of fractal theory appearance. Physics of Wave Processes and Radio Systems. 2021;24(2):113–126 (in Russian). DOI: 10.18469/1810-3189.2021.24.2.113-126.
Received: 
17.03.2025
Accepted: 
12.05.2025
Available online: 
19.06.2025
Published: 
30.09.2025
  • 1071 reads