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Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution

Author

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  • Victor Orlov

    (Institute of Digital Technologies and Modeling in Construction, Moscow State University of Civil Engineering, Yaroslavskoye Shosse, 26, 129337 Moscow, Russia)

Abstract

The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular points in the real domain was obtained. The proof of existence and uniqueness is based on an author’s modification of the technology of the classical Cauchy theorem. A priori estimates of the analytical approximate solution in the vicinity of a moving singular point are obtained. Calculations of a numerical experiment are presented.

Suggested Citation

  • Victor Orlov, 2023. "Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution," Mathematics, MDPI, vol. 11(4), pages 1-7, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:873-:d:1062386
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    Cited by:

    1. Valery Pupin & Victor Orlov, 2023. "Mathematical Calculation of Synchronous Electric Motors Dynamic Stability," Mathematics, MDPI, vol. 11(21), pages 1-17, October.

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