Abstract:
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. This article provides 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 formalization of hysteresis dependencies. The first section of the work is devoted to a description of the input-output correspondences of the classical converter of continual systems of relays, its main properties are established, methods for constructing the output using the formalism of the demagnetization function are described, and a generalization of the classical converter of continual system of relays to the case of vector input-output correspondences is given. Applications of the Preisach model, classified according to various natural science fields, are given in the second section. Various generalizations of the model as applied to systems containing ferromagnetic and ferroelectric materials are described there. The main attention was paid to experimental works, where the model of continual system of relays was used to analytically describe the dependences observed in experiments. Special attention in the review is paid to technical applications of the model such as energy storage devices, systems using the piezoelectric effect, models of systems with long-term memory. The review also presents the results of using the converter of continual systems of relays in biology and medicine, as well as in economics. The third part of the review describes the properties of the converter of continual system of relays in terms of its response to stochastic external influences and provides a generalization of the converter model to the case of stochasticity of the 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: a method for identifying dynamic modes is given, based on a modification of Benettin's algorithm for calculating Lyapunov exponents in systems with nonsmooth multivalued characteristics.
Keywords:hysteresis, non-ideal relay, continual systems of relays, converter of CSR, stochastic input, sales rate, price function, consumer behaviour.
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