Mathematical views of the fractional Chua’s electrical circuit described by the Caputo-Liouville derivative
Abstract This paper revisits Chua’s electrical circuit in the context of the Caputo-Liouville fractional derivative. We introduce the Caputo-Liouville fractional derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua’s electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua’s electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedad Mexicana de Física
2021
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| Online Access: | http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2021000100011 |
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| Summary: | Abstract This paper revisits Chua’s electrical circuit in the context of the Caputo-Liouville fractional derivative. We introduce the Caputo-Liouville fractional derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua’s electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua’s electrical circuits go in the same way. The graphical representations have supported all the main results of the paper. |
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