Microcontroller Implementation, Controls, and Synchronization of Three-Dimensional Autonomous System with a Parabolic Equilibrium Point

The microcontroller implementation, controls, and synchronization of a three-dimensional (3D) autonomous system with a parabolic equilibrium point are investigated in this paper. The system in question displays a reverse period doubling route hidden chaotic attractors with two different shapes. Then...

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Bibliographic Details
Published in:Mathematical problems in engineering 2022-11, Vol.2022, p.1-11
Main Authors: Dianorre, Tokoue Ngatcha, Eric Donald, Dongmo, Jules, Metsebo, Saeed, Nasr, Alex Stephane, Kemnang Tsafack, Hubert, Boudoue Malwe
Format: Article
Language:English
Subjects:
Active control
Chaos theory
Control methods
Equilibrium
Error feedback
Microcontrollers
Parameters
Period doubling
Simulation
Sliding mode control
Synchronism
Variables
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Summary:The microcontroller implementation, controls, and synchronization of a three-dimensional (3D) autonomous system with a parabolic equilibrium point are investigated in this paper. The system in question displays a reverse period doubling route hidden chaotic attractors with two different shapes. Then, the partial and total amplitude controls of the system are achieved by inserting two parameters. A microcontroller implementation is performed in order to confirm the results obtained from the numerical simulations. It is found that the results from the numerical simulations and microcontroller implementation qualitatively agree with each other. The sliding mode controllers are designed to control chaos in the system under study. With the sliding mode control method, the numerical simulations confirm that chaos can be controlled in the 3D autonomous system with a parabolic equilibrium point. In addition, two chaotic 3D autonomous systems with a parabolic equilibrium point and the same parameters are synchronized by the use of a unidirectional linear error feedback coupling scheme. Finally, an active control technique is applied to bring about chaos synchronization between two chaotic 3D autonomous systems with a parabolic equilibrium and different parameters.
ISSN:1024-123X
1563-5147
DOI:10.1155/2022/7804440