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Estimates Of Frequency Of Periodic Regimes For Phase Synchronization Systems With Distributed Parameters

The journal version of this paper is published in Cybernetics And Physics, Vol.4, Is.2, 2015
Vera Smirnova, Alexander Shepeljavyi, Natalia Utina, Aleksey Perkin
Many systems, arising in electrical and electronic engineering
are based on controlled phase synchronization of several periodic processes (``phase synchronization'' systems, or PSS). Typically such systems are featured by the \emph{gradient-like behavior}, i.e.
any solution of the system converges to one of equilibrium points.
If a PSS in not gradient-like it may have periodic regimes which are undesirable for most systems.
In the present paper, we address the problem of lack or existence of periodic regimes for phase synchronization systems described by integro-differential Volterra equations.
New effective frequency--algebraic estimates for the frequency of possible periodic regimes are obtained by means of Fourier expansions and the tool of Popov functionals destined specially for periodic nonlinearities.
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