maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2025-4-316-328mais-1978Research ArticleComputing Methodologies and ApplicationsМоделирование скрытого аттрактора в системе Чуа на основе аналоговой схемы с операционными усилителямиModeling of a hidden attractor in the Chua system based on an analog circuit with operational amplifiershttps://orcid.org/0000-0003-4136-1227ПчелинцевАлександр НиколаевичPchelintsevAlexander N.pchelintsev.an@yandex.ruТамбовский государственный технический университетРоссияTambov State Technical UniversityRussian Federation202505122025324316328Copyright © Пчелинцев А.Н., 20252025Пчелинцев А.Н.Pchelintsev A.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1978

В статье рассматривается аналоговая схема (аналоговый компьютер), в которой динамика изменения напряжений описывается системой Чуа. Найдены начальные состояния (установка начальных напряжений), которые выводят схему на предельный режим работы — скрытый аттрактор — устойчивый предельный цикл с частотой $\approx0.5$ Гц. При этом получаемые сигналы имеют форму, близкую к гармоническому сигналу. Разработанная схема-генератор колебаний содержит семь операционных усилителей, не имеет мемристора, что дает значительное удешевление стоимости сборки; не имеет катушек индуктивности, что устраняет проблемы их изготовления, и гираторов. Определены значения номиналов сопротивлений и емкостей, соответствующих рассматриваемым параметрам системы. Один из инверторов схемы на базе операционного усилителя моделирует нелинейность типа упора, присутствующую в системе Чуа, периодически входя в состояния насыщения. После сборки устройства выходные сигналы схемы, соответствующие фазовым координатам системы Чуа, записаны в текстовый файл через шаг по времени с помощью цифрового осциллографа. Уточнены (идентифицированы) параметры математической модели в разработанной автором компьютерной программе, проверена адекватность модели по коэффициенту детерминации и критерию Фишера. Также численно исследуя устойчивость по Пуассону найденного режима в системе Чуа, определен период и частота полученного цикла, проведено сравнение с частотой, которую дает цифровой осциллограф.

In the article, the author considers an analog circuit (analog computer) in which the dynamics of voltage changes is described by the Chua system. The initial states (setting the initial voltages) are found which bring the circuit to the limit mode of operation (a hidden attractor): a stable limit cycle with a frequency of $\approx0.5$ Hz. In this case, the received signals have a shape close to a harmonic signal. The developed oscillation generator circuit contains seven operational amplifiers, does not have a memristor which significantly reduces the cost of assembly, inductors which eliminates the problems of their manufacture, and gyrators. The values of the resistance and capacitance ratings corresponding to the considered system parameters are deter-mined. One of the inverters of the circuit based on the operational amplifier models the nonlinearity of the stop type, present in the Chua system, periodically entering saturation states. After assembling the device, the output signals of the circuit corresponding to the phase coordinates of the Chua system are recorded in the text file in time steps using a digital oscilloscope. The parameters of the mathematical model in the computer program developed by the author are identified, the adequacy of the model is checked by the coefficient of determination and the Fisher criterion. Also, by numerically investigating the Poisson stability of the found mode in the Chua system, the period and frequency of the obtained cycle are determined, and a comparison is made with the frequency given by the digital oscilloscope.

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The authors declare that there are no conflicts of interest present.