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The Existence of a Unique Fixed Point of Mappings Generated by a Multidimensional System with Relay Hysteresis

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Abstract

A multidimensional system of ordinary differential equations with relay hysteresis is considered. The system parameters are assumed to be such that there exists a family of continuous operators each of which maps some connected compact set into itself. In this case, the operator corresponds to a periodic orbit with an even number of switching points in the phase space of the system. For the operator family, a necessary and sufficient condition for the existence of a single fixed point is obtained.

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Funding

This work was financially supported by the Russian Science Foundation, project 23-21-00069, https://rscf.ru/en/project/23-21-00069/.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    A. M. Kamachkin, V. V. Yevstafyeva & D. K. Potapov

Authors
  1. A. M. Kamachkin
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  2. V. V. Yevstafyeva
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  3. D. K. Potapov
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Corresponding authors

Correspondence to A. M. Kamachkin, V. V. Yevstafyeva or D. K. Potapov.

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Translated by V. Potapchouck

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Kamachkin, A.M., Yevstafyeva, V.V. & Potapov, D.K. The Existence of a Unique Fixed Point of Mappings Generated by a Multidimensional System with Relay Hysteresis. Diff Equat 59, 998–1002 (2023). https://doi.org/10.1134/S0012266123070121

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  • DOI: https://doi.org/10.1134/S0012266123070121

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