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Chaos Theory, Fractals and Scaling in the Radar: A Look from 2015

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The Foundations of Chaos Revisited: From Poincaré to Recent Advancements

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Results of application of theory of fractal and chaos, scaling effects and fractional operators in the fundamental issues of the radio location and radio physic are presented in this report. The key point is detection and processing of super weak signals against the background of non-Gaussian intensive noises and strays. An alternative—the radar range is increased dramatically. The results of researches of spectrum fractal dimensions of lightning discharge in the middle atmosphere at attitudes from 20 to 100 km which are above the majority of clouds are presented. The author has been investigating these issues for exactly 35 years and has obtained results of the big scientific and practical worth. The reader is invited to look at the fundamental problems with the synergetic point of view of non-Markovian micro- and macro systems.

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References

  1. C.A. Rogers, Hausdorff Measures (Cambridge University Press, London, 1970), 179 pp

  2. K.B. Oldham, J. Spanier, The Fractional Calculus (Academic, New York, 1974), 234 pp

    Google Scholar 

  3. B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freeman and Co., San Francisco, 1983), 460 pp

    Google Scholar 

  4. A.A. Potapov, Fractals in Radiophysics and Radar (Logos, Moscow, 2002), 664 pp

    Google Scholar 

  5. A.A. Potapov, Fractals in Radiophysics and Radar: Topology of a Sample (Universitetskaya Kniga, Moscow, 2005), 848 pp

    Google Scholar 

  6. A.A. Potapov, R.M. Crownover, Introduction to Fractals and Chaos (Tekhnosfera, Moscow, 2006), pp. 374–479

    Google Scholar 

  7. A.A. Potapov, Y.V. Gulyaev, S.A. Nikitov, A.A. Pakhomov, V.A. German, in Newest Images Processing Methods, ed. by A.A. Potapov (FIZMATLIT, Moscow, 2008), 496 pp

    Google Scholar 

  8. A.A. Potapov, V.A. Chernykh, A. Letnikov, Fractional Calculus in the Physics of Fractals (LAMBERT Academic Publishing, Saarbrücken, 2012), 688 pp

    Google Scholar 

  9. A.A. Potapov, in The Textures, Fractal, Scaling Effects and Fractional Operators as a Basis of New Methods of Information Processing and Fractal Radio Systems Designing. Proceedings of SPIE, vol. 7374 (Society of Photo-optical Instrumentation Engineers, Bellingham, 2009), pp. 73740E-1–73740E-14

    Google Scholar 

  10. A.A. Potapov, Fractal Method and Fractal Paradigm in Modern Natural Science (Nauchnaya Kniga, Voronezh, 2012), 108 pp

    Google Scholar 

  11. S.A. Podosenov, A.A. Potapov, J. Foukzon, E.R. Menkova, in Nonholonomic, Fractal and Linked Structures in Relativistic Continuous Medium, Electrodynamics, Quantum Mechanics and Cosmology, 3 vols., ed. by A.A. Potapov (ENAND, Moscow, 2015), 1128 pp

    Google Scholar 

  12. A.A. Potapov, in Fractals and Scaling in the Radar: A Look from 2015, Book of Abstracts 8nd International Conference (CHAOS’ 2015) on Chaotic Modeling, Simulation and Applications, Henri Poincaré Institute, Paris, 26–29 May 2015, p. 102

    Google Scholar 

  13. A.А. Potapov, in New Conception of Fractal Radio Device with Fractal Antennas and Fractal Detectors in the MIMO—Systems. Book of Abstracts Third International Scientific Symposium “The Modeling of Nonlinear Processes and Systems (MNPS-2015)”, Moscow, 22–26 June 2015, p. 33

    Google Scholar 

  14. A.A. Potapov, in Features of Multi-Fractal Structure of the High-Attitude Lightning Discharges in the Ionosphere: Elves, Jets, Sprites, Book of Abstracts 8nd International Conference (CHAOS’ 2015) on Chaotic Modeling, Simulation and Applications, Henri Poincaré Institute, Paris, 26–29 May 2015, pp. 101–102

    Google Scholar 

  15. J. Yang, F. GuiLi, A gigantic jet event observed over a thunderstorm in mainland China. Chin. Sci. Bull. 57(36), 4791–4800 (2012)

    Article  Google Scholar 

  16. A.A. Potapov, V.A. German, Detection of artificial objects with fractal signatures. Pattern Recognit. Image Anal. 8(2), 226–229 (1998)

    Google Scholar 

  17. F.G. Bass, I.M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon Press, Oxford, 1978)

    Google Scholar 

  18. N. Lin, H.P. Lee, S.P. Lim, K.S. Lee, Wave scattering from fractal surfaces. J. Mod. Opt. 42, 225–241 (1995)

    Article  ADS  Google Scholar 

  19. A.A. Potapov, A.V. Laktyunkin, Theory of the wave scattering by anisotropic fractal surface. Nonlinear World 6(1), 3–35 (2008)

    Google Scholar 

  20. A.A. Potapov, The theory of functionals of stochastic backscattered fields. J. Commun. Technol. Electron. 52, 245–292 (2007)

    Article  Google Scholar 

  21. A.A. Potapov, A.V. Laktyun’kin, Frequency coherence function of a space–time radar channel forming images of an anisotropic fractal surface and fractal objects. J. Commun. Technol. Electron. 60, 962–969 (2015)

    Article  Google Scholar 

  22. M.V. Berry, Z.V. Blackwell, Diffractal echoes. J. Phys. A: Math. Gen. 14, 3101–3110 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  23. A.A. Potapov, The base of fractal antenna theory and applications: utilizing in electronic devices, in Proceedings of the 2013 IX International Conference on Antenna Theory and Techniques (16–20 September 2013, Odessa, Ukraine). Odessa National A.S. Popov Academy of Telecommunications, Odessa, 2013, p. 62–67

    Google Scholar 

  24. A.A. Potapov, The global fractal method and the fractal paradigm in fundamental radar problems, in Book of Abstracts International Conference on Dynamics, Bifurcations and Strange Attractors. Dedicated to the Memory of L.P. Shil’nikov (1934–2011) (1–5 July 2013, Nizhni Novgorod, Russia). Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, 2013, p. 98

    Google Scholar 

  25. A.A. Potapov, Oscillator with fractional differential positive feedback as model of fractal dynamics. J. Comput. Intell. Electron. Syst. 3, 236–237 (2014)

    Google Scholar 

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Potapov, A.A. (2016). Chaos Theory, Fractals and Scaling in the Radar: A Look from 2015. In: Skiadas, C. (eds) The Foundations of Chaos Revisited: From Poincaré to Recent Advancements. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-29701-9_12

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