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Article

A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

1
Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72000, Mexico
2
Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
3
Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran
4
Department of Electrical Engineering, University of Dschang, P.O. Box 134 Dschang, Cameroon
5
Center for Nonlinear Dynamics, Defence University, P.O.Box 1041 Bishoftu, Ethiopia
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(8), 564; https://doi.org/10.3390/e20080564
Received: 2 July 2018 / Revised: 23 July 2018 / Accepted: 25 July 2018 / Published: 28 July 2018
In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics. View Full-Text
Keywords: hidden attractor; self-excited attractor; fractional order; spectral entropy; coexistence; multistability hidden attractor; self-excited attractor; fractional order; spectral entropy; coexistence; multistability
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MDPI and ACS Style

Munoz-Pacheco, J.M.; Zambrano-Serrano, E.; Volos, C.; Jafari, S.; Kengne, J.; Rajagopal, K. A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors. Entropy 2018, 20, 564. https://doi.org/10.3390/e20080564

AMA Style

Munoz-Pacheco JM, Zambrano-Serrano E, Volos C, Jafari S, Kengne J, Rajagopal K. A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors. Entropy. 2018; 20(8):564. https://doi.org/10.3390/e20080564

Chicago/Turabian Style

Munoz-Pacheco, Jesus M., Ernesto Zambrano-Serrano, Christos Volos, Sajad Jafari, Jacques Kengne, and Karthikeyan Rajagopal. 2018. "A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors" Entropy 20, no. 8: 564. https://doi.org/10.3390/e20080564

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