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Complex dynamics of a simple distributed self-oscillatory model system with delay

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Abstract

A simple model for a distributed self-oscillatory system with cubic nonlinearity and delay is presented. Conditions for oscillation self-excitation and stationary oscillation conditions, as well as the stability of the oscillations, are analyzed. Nonstationary self-modulation regimes (including conditions of complex dynamics and chaos) are simulated numerically over a wide range of control parameters. As the factor of nonequilibrium grows, regular and chaotic regimes alternate in a complex manner. The transitions to chaos may follow all scenarios known for finite-dimensional systems. The model suggested is somewhat akin to a number of earlier finite-dimensional models aimed at studying mode competition in resonance electron masers.

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Authors and Affiliations

  1. Saratov State University, ul. Moskovskaya 155, Saratov, 410026, Russia

    N. M. Ryskin & A. M. Shigaev

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  1. N. M. Ryskin
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  2. A. M. Shigaev
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__________

Translated from Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 72, No. 7, 2002, pp. 1–8.

Original Russian Text Copyright © 2002 by Ryskin, Shigaev.

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Ryskin, N.M., Shigaev, A.M. Complex dynamics of a simple distributed self-oscillatory model system with delay. Tech. Phys. 47, 795–802 (2002). https://doi.org/10.1134/1.1495037

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