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

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Chetverikov A. P., Frolova N. B. Dynamics of interaction of linear wave and a wave with inertial nonlinearity under influence of noise. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 1, pp. 82-97. DOI: 10.18500/0869-6632-2006-14-1-82-97

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Dynamics of interaction of linear wave and a wave with inertial nonlinearity under influence of noise

Chetverikov Aleksandr Petrovich, Saratov State University
Frolova Natalja Borisovna, Saratov State University

The results of numerical simulation of oscillations in a simple model of interaction of waves with inertial nonlinearity applicable to study of phenomena in a backward wave oscillator are produced. Convenient numerical characteristics for identification of anharmonic oscillations – a decrement of the autocorrelation function and the characteristic correlation time – have been used. It has been found that both sophistication and ordering of an excited signal were possible under influence of additive noise. The dependence of a critical value of noise intensity at which disintegration of autonomous dynamics of the system on the nonequilibrium parameter of a system has been determined. 

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  1. Electronics of backwave lamps. Ed. Shevchik VN, Trubetskov DI. Saratov: Saratov University Publishing; 1975. 194 p. (In Russian).
  2. Ginzburg NS, Kuznetsov SP, Fedoseeva TN. Theory of transients in relativistic backward-wave tubes. Radiophysics and Quantum Electronics. 1978;21(7):728–739. DOI: 10.1007/BF01033055.
  3. Chetverikov AP. Periodic and chaotic self-oscillations in simple distributed electron-wave systems. Bulletin of the Russian Academy of Sciences: Physics. 1994;58(8):171.
  4. Ryskin NM, Titov VN, Trubetskov DI. Transition to the chaotic regime in a system composed of an electron beam and an inverse electromagnetic wave. Doklady Physics. 1998;43(2):90–93.
  5. Chetverikov AP. Nonlinear dynamics of the system of liquid-acting counter electromagnetic waves and electron waves with cubic phase nonlinearity. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(5):46.
  6. Frolova NB, Chetverikov AP. Self-Oscillations In A Backward-Wave Tube In The Presence Of An External Noise. Journal of Communications Technology and Electronics. 2004;49(7):876–881.
  7. Frolova NB, Chetverikov AP. Oscillations in the distributed system of interacting backward waves at the presence of fluctuations. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(5):50–59.
  8. Bezruchko BP, Kuznetsov SP, Trubetskov DI. Experimental observation of stochastic self-oscillations in the electron beam-backscattered electromagnetic wave dynamic system. Journal of Experimental and Theoretical Physics Letters (JETP Letters). 1979;29(3):162–165.
  9. Ginsburg NS, Kuznetsov SP. Periodic and stochastic auto-modulation modes in electronic generators with distributed interaction. Relativistic high-frequency electronics. Problems of increasing the power and frequency of radiation. Gorky: IPFAN USSR; 1981. P. 101. (In Russian).
  10. Garcia-Ojalo J, Sancho JM. Noise in Spatially Extended Systems. New York: Springer–Verlag; 1999. 307 p.
  11. Nikitin NN, Razevig VD. Methods for the digital simulation of stochastic differential equations and an estimate of their errors. U.S.S.R. Comput. Math. Math. Phys. 1978;18(1):102–113. DOI: 10.1016/0041-5553(78)90011-3.
  12. Landa PS. Theory of Fluctuation Transitions and its Applications. Journal of Communications Technology and Electronics. 2001;46(10):1157–1197.
  13. Bezruchko BP, Bulgakova LV, Kuznetsov SP, Trubetskoy DI. Stochastic self-oscillations and instability in the backwave lamp. Radio Engineering and Electronic Physics. 1983;28(6):1136–1139.
  14. Kuznetsov SP, Trubetskov DI. Two lectures on the non-stationary theory of interaction of electron beams with electromagnetic waves. Lectures on microwave electronics. Saratov: Saratov University Publishing; 1974. P. 88. (In Russian).
  15. Kuznetsov SP, Pishchik LA, Trubetskoy DI, Chetverikov AP. Program of numerical modeling of non-stationary processes and self-oscillating modes in LOVO. SVCH-Tekhnika. 1983;4:66.
  16. Kuznetsov SP, Trubetskov DI. Chaos and hyperchaos in a backward-wave oscillator. Radiophysics and Quantum Electronics. 2004;47(5-6):341–355. DOI: 10.1023/
  17. Malakhov AN. Fluctuations in self-oscillating systems. Moscow: Nauka; 1968. 660 p. (In Russian).
  18. Anishchenko VS, Astakhov VV, Neiman AB, Vadivasova TE, Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Development. Berlin: Springer; 2007. 429 p. (In Russian).
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