Composed perturbations to a coupled ODEs system with hysteresis

Shengda Zeng; Sergey A. Timoshin; Shengda Zeng; Sergey A. Timoshin

doi:10.3934/mine.2025021

Mathematics in Engineering

2025, Volume 7, Issue 4: 505-521. doi: 10.3934/mine.2025021

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Composed perturbations to a coupled ODEs system with hysteresis

Shengda Zeng ¹,
Sergey A. Timoshin ^{2
,
,}

1.
National Center for Applied Mathematics in Chongqing, and School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
2.
School of Mathematics and Physics, Xi'an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, China
^‡Dedicated to Pavel Krejčí on the occasion of his 70th birthday.

Received: 27 December 2024 Revised: 29 June 2025 Accepted: 21 August 2025 Published: 26 August 2025

In this paper, we address a system of two ODEs including a hysteresis nonlinearity of generalized play type. Our system is subject to a composed perturbation, giving under particular choices of composants various types of common multivalued perturbations. We prove the existence of a solution to this system. The theoretical analysis is complemented by a discussion of a mechanical model illustrating potential applicability of our results and the physical meaning of the underlying assumptions.
- evolution system,
- hysteresis,
- composed perturbation,
- nonconvex-valued set-mapping,
- convex-valued set-mapping,
- mechanical system
Citation: Shengda Zeng, Sergey A. Timoshin. Composed perturbations to a coupled ODEs system with hysteresis[J]. Mathematics in Engineering, 2025, 7(4): 505-521. doi: 10.3934/mine.2025021

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Abstract

In this paper, we address a system of two ODEs including a hysteresis nonlinearity of generalized play type. Our system is subject to a composed perturbation, giving under particular choices of composants various types of common multivalued perturbations. We prove the existence of a solution to this system. The theoretical analysis is complemented by a discussion of a mechanical model illustrating potential applicability of our results and the physical meaning of the underlying assumptions.

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