A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation
In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibr...
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doaj-8e6d1d6701fb4b38846f0050127e72162021-09-26T00:27:17ZengMDPI AGInventions2411-51342021-07-016494910.3390/inventions6030049A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital ImplementationZain-Aldeen S. A. Rahman0Basil H. Jasim1Yasir I. A. Al-Yasir2Raed A. Abd-Alhameed3Bilal Naji Alhasnawi4Department of Electrical Techniques Institute/Qurna, Southern Technical University, Basra 61016, IraqDepartment of Electrical Engineering, College of Engineering, University of Basrah, Basra 61004, IraqBiomedical and Electronics Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UKBiomedical and Electronics Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford BD7 1DP, UKDepartment of Electrical Engineering, College of Engineering, University of Basrah, Basra 61004, IraqIn this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.https://www.mdpi.com/2411-5134/6/3/49fractional orderdynamicschaoticsystemsynchronizationarduino due |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zain-Aldeen S. A. Rahman Basil H. Jasim Yasir I. A. Al-Yasir Raed A. Abd-Alhameed Bilal Naji Alhasnawi |
spellingShingle |
Zain-Aldeen S. A. Rahman Basil H. Jasim Yasir I. A. Al-Yasir Raed A. Abd-Alhameed Bilal Naji Alhasnawi A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation Inventions fractional order dynamics chaotic system synchronization arduino due |
author_facet |
Zain-Aldeen S. A. Rahman Basil H. Jasim Yasir I. A. Al-Yasir Raed A. Abd-Alhameed Bilal Naji Alhasnawi |
author_sort |
Zain-Aldeen S. A. Rahman |
title |
A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation |
title_short |
A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation |
title_full |
A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation |
title_fullStr |
A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation |
title_full_unstemmed |
A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation |
title_sort |
new no equilibrium fractional order chaotic system, dynamical investigation, synchronization, and its digital implementation |
publisher |
MDPI AG |
series |
Inventions |
issn |
2411-5134 |
publishDate |
2021-07-01 |
description |
In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications. |
topic |
fractional order dynamics chaotic system synchronization arduino due |
url |
https://www.mdpi.com/2411-5134/6/3/49 |
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