Title: The electrical circuit of a new seven-dimensional system with 21 boundaries and the phenomenon of complete synchronisation
Authors: Khaled Mohammed Al-Hamad; Anas Romaih Obaid; Ahmed S. Al-Obeidi
Addresses: Gifted School of Nineveh, Directorate of Education, Mosul, Iraq ' Gifted School of Nineveh, Directorate of Education, Mosul, Iraq ' Specialty of Mathematics, Gifted School of Nineveh, Directorate of Education, Mosul, Iraq
Abstract: One the most important properties of the dynamical system is the complete synchronisation phenomenon. In this document, we are working on creating a non-linear controller for the success of the synchronisation process between two identical systems, each of them seven-dimensional. The linearisation and Lyapunov methods have been used as analytical methods to demonstrate the phenomenon. The results showed that the linearisation method does not need to update the function as in the Lyapunov method, and therefore it is effective to achieve synchronisation phenomenon with better results than the Lyapunov method. Digital emulation was applied to the mathematical system with control system and the error dynamical system, the results are excellent. We've studied complete synchronisation phenomenon according to Lyapunov and linearisation, and compared their results. Finally, we applied the current system and presenting it in a new attractor and compare these results with other similar ones.
Keywords: chaos; Lyapunov; linearisation; complete synchronisation; non-linear dynamical system.
International Journal of Computer Applications in Technology, 2022 Vol.68 No.3, pp.269 - 276
Received: 07 Apr 2021
Accepted: 07 Jun 2021
Published online: 18 Aug 2022 *