This article is cited in 7 papers

MATHEMATICS

Hidden boundary of global stability in the Kapranov conjecture on the pull-in range

N. Kuznetsov^ab, M. Yu. Lobachev^a, T. N. Mokaev<sup>a

a</sup> Saint Petersburg State University
^b Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg

Abstract: Within the framework of the development of the theory of hidden oscillations, the problem of determining the boundary of global stability and revealing its hidden parts corresponding to the non-local birth of hidden oscillations is considered. For a phase-locked loop with a proportional-integrating filter and a piecewise-linear phase detector characteristic, effective methods for determination of bifurcations of the global stability loss, for obtaining analytical formulas of the bifurcation values, and for constructing trivial and hidden parts of the global stability boundary are suggested.

Keywords: hidden boundary of global stability, self-excited and hidden oscillations, local and global bifurcations, phase-locked loop, Kapranov conjecture, pull-in range.

UDC: 531.36:534.1

Received: 25.02.2023
Revised: 12.05.2023
Accepted: 22.05.2023

DOI: 10.31857/S2686954323600106

 English version: Doklady Mathematics, 2023, 108:1, 300–308

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