First-Kind Cycles of Systems with Cylindrical Phase Space

Abstract

In this paper, we consider a system of differential equations with a cylindrical phase space, which is a mathematical model of a phase-locked loop system. Conditions of the existence of limit cycle of the first kind are obtained.

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Correspondence to S. S. Mamonov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 148, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory” (Ryazan, September 15–18, 2016), 2018.

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Mamonov, S.S., Kharlamova, A.O. First-Kind Cycles of Systems with Cylindrical Phase Space. J Math Sci 248, 457–466 (2020). https://doi.org/10.1007/s10958-020-04886-y

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Keywords

  • limit cycle of the first kind
  • cylindrical phase space
  • positively invariant set
  • toroidal set

AMS Subject Classification

  • 34K05
  • 34K13
  • 34K60