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On Forced Oscillations in a Relay System with Hysteresis

  • NONLINEAR SYSTEMS
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Abstract

This paper discusses the phenomenon associated with the forced synchronization (“entrainment of a self-sustained oscillator by an external force”) in a relay system with hysteresis, which manifests itself in the occurrence of periodic motions close to the rhythmic activity of neurons, when packets of fast oscillations are interspersed with intervals of the slow dynamics. To study this phenomenon, we introduce a circle mapping, which, depending on the parameters, can be a circle diffeomorphism or discontinuous map (“gap map”). In both cases, this mapping demonstrates the so-called period-adding bifurcation structure. It is demonstrated that packets number of fast oscillations in the period of periodic motion is determined by the rotation number, and the length of the intervals between the packets may be found of the boundaries of the absorbing interval. The change in the number of pulses in the packet occurs through the border-collision bifurcation.

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Funding

Zh.T. Zhusubaliyev was supported by the Ministry of Education and Science of the Russian Federation within the scope of the “Implementation of the Strategic Academic Leadership, program Priority 20302” (1.73.23 II; 1.7.21/S-2, 1.7.21/4-24-7). U.A. Sopuev was supported by the Osh State University (grant nos. 14-22; 19-24). The work of D.A. Bushuev was supported within the framework of the Program “Priority-2030” using equipment of High Technology Center of the Belgorod State Technological University named after V.G. Shukhov.

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Authors and Affiliations

  1. Southwest State University, Kursk, Russia

    Zh. T. Zhusubaliyev

  2. Osh State University, Osh, Kyrgyzstan

    U. A. Sopuev

  3. Belgorod State Technological University named after V.G. Shukhov, Belgorod, Russia

    D. A. Bushuev

Authors
  1. Zh. T. Zhusubaliyev
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  2. U. A. Sopuev
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  3. D. A. Bushuev
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Correspondence to Zh. T. Zhusubaliyev, U. A. Sopuev or D. A. Bushuev.

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This paper was recommended for publication by N. V. Kuznetsov, a member of the Editorial Board

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Zhusubaliyev, Z.T., Sopuev, U.A. & Bushuev, D.A. On Forced Oscillations in a Relay System with Hysteresis. Autom Remote Control 85, 377–386 (2024). https://doi.org/10.1134/S0005117924040088

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  • DOI: https://doi.org/10.1134/S0005117924040088

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