Hybrid simulation of the Rossler system by synchronizing analog and discrete models
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
Article was received:12-11-2018
This article written in Russian. You can find full text of article in Russian here .
The journal allows the author(s) to hold the copyright without restrictions. All authors automatically own full copyright in their work as soon as they create it, and current Russian Federal legislation protects them.
Licence type: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
The journal is an open access journal which means that everybody can read, download, copy, distribute, print, search, or link to the full texts of these articles in accordance with Creative Commons Attribution- NonCommercial 4.0 International License.
You are free to:
Share — copy and redistribute the material in any medium or format.
Adapt — remix, transform, and build upon the material The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
NonCommercial — You may not use the material for commercial purposes.
No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.