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

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Kornienko V. N., Privezencev A. P. Fractional brownian motion in virtual cathode discrete models. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 4, pp. 114-123. DOI: 10.18500/0869-6632-2003-11-4-114-123

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Fractional brownian motion in virtual cathode discrete models

Kornienko Vladimir Nikolaevich, Kotel'nikov Institute of Radioengineering and Electronics of Russian Academy of Sciences
Privezencev Aleksej Pavlovich, National Research Tomsk State University

Results of modeling virtual cathode dynamics for the determined flat sheet model and simple probabilistic model have been compared. It has been shown that stochastic component of mass center motion is formed as fractional Brownian motion for both the stochastic and determined models.

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  1. Privezentsev AP, Fomenko GP. Complex dynamics of charged particle flow with a virtual cathode. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(5):56-68 (in Russian).
  2. Anfinogentov VG. Chaotic oscillations in an electron flow with a virtual cathode. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(5):69-83 (in Russian).
  3. Privezentsev AP, Cherepenin VA. Fractal properties of virtual cathode oscillations. J. Commun. Technol. Electron. 1998;43(6):738-742 (in Russian).
  4. Nikolis G, Prigogine I. Cognition of the Complex. Moscow: Mir; 1990. 342 p. (in Russian).
  5. Gvozdover SD. Theory of Electronic Devices of Ultrahigh Frequencies. Moscow: GosTechTeorizdat; 1956. 528 p. (in Russian).
  6. Koronovskii AA, Khramov AB, Anfinogentov VG. Phenomenological model of electron flow with a virtual cathode. Bulletin of the Russian Academy of Sciences: Physics. 1999;63(12):2355-2361 (in Russian).
  7. Norman GE, Polak LS. Irreversibility in classical statistical mechanics. Proc. Acad. Sci. USSR. 1982;263(2):337-340 (in Russian).
  8. Prigogine I. From Being to Becoming: Time and Complexity in the Physical Sciences. W H Freeman & Co; 1981. 272 p.
  9. Anfinogentov VG, Koronovskii AA, Khramov AE. Some models of the class of lattice gases related to the description of population sizes. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(4):74 (in Russian).
  10. Bak P, Tang C, Wiesenfeld K. Self-organized criticality. Phys. Rev. А. 1988;38(1):364-374. DOI: 10.1103/PhysRevA.38.364.
  11. Kornienko BH, Privezentsev AP. Available from: http:/
  12. Feller Ц. Introduction to Probability Theory and Its Applications. Wiley; 1968. 509 p.
  13. Privezentsev AP, Sablin NI, Fomenko GP. Hysteresis of oscillatory modes of a virtual cathode in drift space. Sov. J. Commun. Technol. Electron. 1989;33(3):659.
  14. Kronover RM. Fractals and Chaos in Dynamic Systems. Fundamentals of Theory. Moscow: Postmarket; 2000. 352 p. (In Russian).
  15. Feder E. Fractals. New York: Springer; 1988. 284 p. DOI: 10.1007/978-1-4899-2124-6.
  16. Potapov AA. Fractals in Radiophysics and Radar. Moscow: Logos; 2002. 664 p. (in Russian).
  17. Bochkov GN, Kuzovlev YE. New aspects in 1/f noise studies. Sov. Phys. Usp. 1983;26(9):829–844. DOI: 10.1070/PU1983v026n09ABEH004497.
  18. Schuster HG. Deterministic Chaos. An Introduction. Weinheim: Physik-Verlag; 1984. 220 p.
  19. Hartler G. 1/f noise аs superposition оf random walks through discrete sets. AIP Conference Proceedings. 2000;511(1):130-135. DOI: 10.1063/1.60021.
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