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<p>The converter of continual systems of relays (also known as the Preisach converter) is a well-known model applicable to describe the hysteresis relationships of a wide range. In this paper, we provide a review of works devoted to the study of systems from various subject areas (physics, economics, biology) where the continual system of relays plays a key role in the description of hysteresis dependencies. In the first section, we consider of the input-output correspondences of the classical converter of continual systems of relays, establish its main properties, describe methods for constructing the output using the formalism of the demagnetization function, and give a generalization of the classical converter of continual system of relays to the case of vector input-output correspondences. In the second section, we give applications of the Preisach model, classified according to various natural science fields. There we describe various generalizations of the model applied to systems containing ferromagnetic and ferroelectric materials. In our review, we focus on experimental works, where the model of continual system of relays was used to analytically describe the dependencies observed in experiments. We pay special attention to technical applications of the model such as energy storage devices, systems using the piezoelectric effect, and models of systems with long-term memory. We also present the results of using the converter of continual systems of relays in biology and medicine, as well as in economics. In the third section, we describe the properties of the converter of continual system of relays in terms of its response to stochastic external influences and consider a generalization of the converter model to the case of stochastic threshold numbers of its elementary components. In addition, the review contains fresh results in the field of dynamics of systems with a converter of continual system of relays: we give a method for identifying dynamic modes based on a modification of Benettin’s algorithm for calculating Lyapunov exponents in systems with nonsmooth multivalued characteristics.</p>

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CONTINUAL SYSTEMS OF RELAYS

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • M. E. Semenov,
  • S. V. Borzunov,
  • O. I. Kanischeva,
  • A. I. Proshunin,
  • P. A. Meleshenko

摘要

The converter of continual systems of relays (also known as the Preisach converter) is a well-known model applicable to describe the hysteresis relationships of a wide range. In this paper, we provide a review of works devoted to the study of systems from various subject areas (physics, economics, biology) where the continual system of relays plays a key role in the description of hysteresis dependencies. In the first section, we consider of the input-output correspondences of the classical converter of continual systems of relays, establish its main properties, describe methods for constructing the output using the formalism of the demagnetization function, and give a generalization of the classical converter of continual system of relays to the case of vector input-output correspondences. In the second section, we give applications of the Preisach model, classified according to various natural science fields. There we describe various generalizations of the model applied to systems containing ferromagnetic and ferroelectric materials. In our review, we focus on experimental works, where the model of continual system of relays was used to analytically describe the dependencies observed in experiments. We pay special attention to technical applications of the model such as energy storage devices, systems using the piezoelectric effect, and models of systems with long-term memory. We also present the results of using the converter of continual systems of relays in biology and medicine, as well as in economics. In the third section, we describe the properties of the converter of continual system of relays in terms of its response to stochastic external influences and consider a generalization of the converter model to the case of stochastic threshold numbers of its elementary components. In addition, the review contains fresh results in the field of dynamics of systems with a converter of continual system of relays: we give a method for identifying dynamic modes based on a modification of Benettin’s algorithm for calculating Lyapunov exponents in systems with nonsmooth multivalued characteristics.