Динамика Гистерезисно-Связанных Осцилляторов Ван-Дер-Поля: Метод Малого Параметра

Медведский, А. Л.; Мелешенко, П. А.; Нестеров, В. А.; Решетова, О. О.; Семенов, М. Е.

doi:10.31857/s0002338821040107

Изв. РАН. Теория и системы упр.

2021

DOI: 10.31857/s0002338821040107

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Динамика Гистерезисно-Связанных Осцилляторов Ван-Дер-Поля: Метод Малого Параметра

А. Л. Медведский¹,

П. А. Мелешенко²,

В. А. Нестеров³

et al.

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Modeling and control of a chaotic process

Tolkachev

2022

Modeling of Systems and Processes

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The article investigates problems related to the control of the dynamics of a system given by the Henon map with a hysteresis component included in it. In particular, possible modifications of the limit set (attractor) of the modified Henon map under hysteresis conditions are studied. The hysteresis element is formalized based on design approach by means of the Preisach model, which is approximated by a system consisting of a finite set of non-ideal relays. To analyze the dynamics, numerical simulation is carried out for various values of the model parameters, which are characterized by chaotic dynamics. For this purpose, a Python script has been developed that simulates the dynamics of the system under hysteresis conditions, and also processes the results to identify dynamic modes. Based on the data obtained, a comparative analysis of strange attractors of the modified and classical Henot mappings is carried out. Next, we study the dynamics depending on the parameters of the modified Henon map. To detect various dynamic regimes, bifurcation diagrams were plotted, the high Lyapunov exponent was calculated based on the Rosenstein algorithm and the 0-1 test was produced depending on the system parameters, and the hysteresis nonlinearity parameter. Established, that hysteresis term regularize dynamics of the system compared to the classical map and changed in the position of bifurcation points in the space of system parameters.

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Modeling and control of a chaotic process

Tolkachev

2022

Modeling of Systems and Processes

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A non-classical optimal control problem with operator hysteresis nonlinearities

Borzunov,

Meleshenko,

Nesterov

et al. 2024

Teoriâ i sistemy upravleniâ

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This article considers a non-classical optimal control problem, in which the dynamics of an object is described by a system of differential operator equations with a hysteresis converter on the right side. The hysteresis dependence is formalized using an analogue of the Preisach converter with inverted threshold numbers, which reflects the nonlinear and multivalued dependence of consumer demand on the price of goods. This allows to take into account the “history” of consumer relations over a finite time interval. The problem of optimal production, storage and sales of products on a mono-commodity market under conditions of a hysteresis demand function has been set and solved. The conditions of solvability of the problem under the conditions of applicability of the maximum principle of L. S. Pontryagin are given. The conditions under which the solution is unique are given. The article also presents the results of computational experiments in which optimal control actions for the model case are identified.

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Динамика Гистерезисно-Связанных Осцилляторов Ван-Дер-Поля: Метод Малого Параметра

Cited by 2 publications

References 0 publications

Modeling and control of a chaotic process

Modeling and control of a chaotic process

A non-classical optimal control problem with operator hysteresis nonlinearities

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