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On the Existence of Oscillatory Modes in a Nonlinear System with Hystereses

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Abstract

We study the existence of oscillatory modes in a controlled nonlinear system closed by a feedback in the form of a bistable hysteretic switch. The system is a simplified mathematical model of a thermal energy harvester. Conditions on the controller and on the system parameters are established that guarantee the existence of oscillatory modes in this system.

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Funding

This work was supported by the Russian Foundation for Basic Research, project nos. 19-57-18006 and 18-07-01283 and the National Science Foundation of Bulgaria, project no. KP-06-Rusiya/21 with the assistance from the Moscow Center for Fundamental and Applied Mathematics.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, China

    A. S. Fursov

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    A. S. Fursov & P. A. Krylov

  3. Bauman Moscow State Technical University, Moscow, 105005, Russia

    A. S. Fursov

  4. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127051, Russia

    A. S. Fursov

  5. Technical University, Sofia, 1000, Bulgaria

    T. S. Todorov & R. P. Mitrev

Authors
  1. A. S. Fursov
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  2. T. S. Todorov
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  3. P. A. Krylov
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  4. R. P. Mitrev
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Corresponding authors

Correspondence to A. S. Fursov, T. S. Todorov, P. A. Krylov or R. P. Mitrev.

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Translated by V. Potapchouck

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Fursov, A.S., Todorov, T.S., Krylov, P.A. et al. On the Existence of Oscillatory Modes in a Nonlinear System with Hystereses. Diff Equat 56, 1081–1099 (2020). https://doi.org/10.1134/S0012266120080108

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  • DOI: https://doi.org/10.1134/S0012266120080108

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