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

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 coexist...
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Autor*in:	Jesus M. Munoz-Pacheco [verfasserIn] Ernesto Zambrano-Serrano [verfasserIn] Christos Volos [verfasserIn] Sajad Jafari [verfasserIn] Jacques Kengne [verfasserIn] Karthikeyan Rajagopal [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability

Übergeordnetes Werk:	In: Entropy - MDPI AG, 2003, 20(2018), 8, p 564
Übergeordnetes Werk:	volume:20 ; year:2018 ; number:8, p 564

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/e20080564

Katalog-ID:	DOAJ029616468

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spelling	10.3390/e20080564 doi (DE-627)DOAJ029616468 (DE-599)DOAJ6c2b200179ff4031a6217d46f269b7be DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Jesus M. Munoz-Pacheco verfasserin aut A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability Science Q Astrophysics Physics Ernesto Zambrano-Serrano verfasserin aut Christos Volos verfasserin aut Sajad Jafari verfasserin aut Jacques Kengne verfasserin aut Karthikeyan Rajagopal verfasserin aut In Entropy MDPI AG, 2003 20(2018), 8, p 564 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:20 year:2018 number:8, p 564 https://doi.org/10.3390/e20080564 kostenfrei https://doaj.org/article/6c2b200179ff4031a6217d46f269b7be kostenfrei http://www.mdpi.com/1099-4300/20/8/564 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2018 8, p 564
allfields_unstemmed	10.3390/e20080564 doi (DE-627)DOAJ029616468 (DE-599)DOAJ6c2b200179ff4031a6217d46f269b7be DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Jesus M. Munoz-Pacheco verfasserin aut A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability Science Q Astrophysics Physics Ernesto Zambrano-Serrano verfasserin aut Christos Volos verfasserin aut Sajad Jafari verfasserin aut Jacques Kengne verfasserin aut Karthikeyan Rajagopal verfasserin aut In Entropy MDPI AG, 2003 20(2018), 8, p 564 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:20 year:2018 number:8, p 564 https://doi.org/10.3390/e20080564 kostenfrei https://doaj.org/article/6c2b200179ff4031a6217d46f269b7be kostenfrei http://www.mdpi.com/1099-4300/20/8/564 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2018 8, p 564
allfieldsGer	10.3390/e20080564 doi (DE-627)DOAJ029616468 (DE-599)DOAJ6c2b200179ff4031a6217d46f269b7be DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Jesus M. Munoz-Pacheco verfasserin aut A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability Science Q Astrophysics Physics Ernesto Zambrano-Serrano verfasserin aut Christos Volos verfasserin aut Sajad Jafari verfasserin aut Jacques Kengne verfasserin aut Karthikeyan Rajagopal verfasserin aut In Entropy MDPI AG, 2003 20(2018), 8, p 564 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:20 year:2018 number:8, p 564 https://doi.org/10.3390/e20080564 kostenfrei https://doaj.org/article/6c2b200179ff4031a6217d46f269b7be kostenfrei http://www.mdpi.com/1099-4300/20/8/564 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2018 8, p 564
allfieldsSound	10.3390/e20080564 doi (DE-627)DOAJ029616468 (DE-599)DOAJ6c2b200179ff4031a6217d46f269b7be DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Jesus M. Munoz-Pacheco verfasserin aut A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability Science Q Astrophysics Physics Ernesto Zambrano-Serrano verfasserin aut Christos Volos verfasserin aut Sajad Jafari verfasserin aut Jacques Kengne verfasserin aut Karthikeyan Rajagopal verfasserin aut In Entropy MDPI AG, 2003 20(2018), 8, p 564 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:20 year:2018 number:8, p 564 https://doi.org/10.3390/e20080564 kostenfrei https://doaj.org/article/6c2b200179ff4031a6217d46f269b7be kostenfrei http://www.mdpi.com/1099-4300/20/8/564 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 20 2018 8, p 564
language	English
source	In Entropy 20(2018), 8, p 564 volume:20 year:2018 number:8, p 564
sourceStr	In Entropy 20(2018), 8, p 564 volume:20 year:2018 number:8, p 564
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institution	findex.gbv.de
topic_facet	hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability Science Q Astrophysics Physics
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container_title	Entropy
authorswithroles_txt_mv	Jesus M. Munoz-Pacheco @@aut@@ Ernesto Zambrano-Serrano @@aut@@ Christos Volos @@aut@@ Sajad Jafari @@aut@@ Jacques Kengne @@aut@@ Karthikeyan Rajagopal @@aut@@
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callnumber-first	Q - Science
author	Jesus M. Munoz-Pacheco
spellingShingle	Jesus M. Munoz-Pacheco misc QB460-466 misc QC1-999 misc hidden attractor misc self-excited attractor misc fractional order misc spectral entropy misc coexistence misc multistability misc Science misc Q misc Astrophysics misc Physics A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors
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topic_title	QB460-466 QC1-999 A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors hidden attractor self-excited attractor fractional order spectral entropy coexistence multistability
topic	misc QB460-466 misc QC1-999 misc hidden attractor misc self-excited attractor misc fractional order misc spectral entropy misc coexistence misc multistability misc Science misc Q misc Astrophysics misc Physics
topic_unstemmed	misc QB460-466 misc QC1-999 misc hidden attractor misc self-excited attractor misc fractional order misc spectral entropy misc coexistence misc multistability misc Science misc Q misc Astrophysics misc Physics
topic_browse	misc QB460-466 misc QC1-999 misc hidden attractor misc self-excited attractor misc fractional order misc spectral entropy misc coexistence misc multistability misc Science misc Q misc Astrophysics misc Physics
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title	A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors
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title_full	A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors
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title_sort	new fractional-order chaotic system with different families of hidden and self-excited attractors
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title_auth	A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors
url	https://doi.org/10.3390/e20080564 https://doaj.org/article/6c2b200179ff4031a6217d46f269b7be http://www.mdpi.com/1099-4300/20/8/564 https://doaj.org/toc/1099-4300
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up_date	2024-07-03T23:40:50.099Z
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A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

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