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Hybrid simulation of the Rossler system by synchronizing analog and discrete models
Butusov Denis Nikolaevich

PhD in Technical Science

Associate Professor, Department of CAD, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197376, Russia, g. Saint Petersburg, ul. Professora Popova, 5

dnbutusov@etu.ru

 

 
Karimov Artur Iskandarovich

PhD in Technical Science

Senior Lecturer, Department of CAD, St. Petersburg State Electrotechnical University "LETI"

197376, Russia, g. Saint Petersburg, ul. Professora Popova, 5

aikarimov@etu.ru
Tutueva Aleksandra Vadimovna

Assistant, Department of CAD, Ulyanov (Lenin) St. Petersburg State Electrotechnical University "LETI"

197376, Russia, Saint Petersburg, ul. Professora Popova, 5

avtutueva@etu.ru

 

 
Krasil'nikov Aleksandr Vital'evich

Assistant, Department of CAD, St. Petersburg State Electrotechnical University "LETI"

197376, Russia, g. Saint Petersburg, ul. Professora Popova, 5

aleksandar7kr@gmail.com
Goryainov Sergei Vadimovich

Engineer, St. Petersburg State Electrotechnical University "LETI"

197376, Russia, g. Saint Petersburg, ul. Professora Popova, 5

svgoryainov@etu.ru
Voznesensky Aleksandr Sergeevich

Engineer, Department of APU, St. Petersburg State Electrotechnical University "LETI"

197376, Russia, g. Saint Petersburg, ul. Professora Popova, 5

a-voznesensky@yandex.ru

Abstract.

The article explores the technology of hybrid modeling of chaotic systems in the form of synchronization of digital and analog models of the Rossler system, interacting via analog-digital and digital-analog conversion paths. The unidirectional and bidirectional variants of chaotic synchronization are considered, and the synchronization error is estimated for each of the specified cases. For the analog implementation of the Rössler system, a circuit has been developed based on operational amplifiers, multipliers, and precision passive elements. The digital model of the system is based on a semi-implicit hardware-oriented method of numerical integration of the second order of algebraic accuracy. In order to substantiate the choice of the method, graphs of the performance of various solvers of ordinary differential equations are presented when simulating the Rössler system. It is shown that the chosen semi-implicit numerical integration method has the highest computational efficiency among all second-order methods. Experimentally demonstrated the ability to synchronize analog and digital models of a chaotic system. The synchronization of two and three models of the Rossler system in various variants of the connection topology is considered. By analyzing the synchronization error, it is shown that the greatest accuracy is achieved when using a fully coupled topology, which is based on the bi-directional synchronization method of the three models of the Rössler system.

Keywords: semi-implicit method, Rossler system, digital-to-analog conversion, chaotic systems, nonlinear dynamics, hybrid model, chaos, chaotic synchronization, digital model, analog model

DOI:

10.7256/2454-0714.2018.4.27828

Article was received:

12-11-2018


Review date:

01-11-2018


Publish date:

14-11-2018


This article written in Russian. You can find full text of article in Russian here .

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