Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control

The objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an...

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Main Authors: Al-Sawalha M. Mossa, Al-Sawalha Ayman
Format: Article
Language:English
Published: De Gruyter 2016-01-01
Series:Open Physics
Subjects:
Online Access:https://doi.org/10.1515/phys-2016-0033
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author Al-Sawalha M. Mossa
Al-Sawalha Ayman
author_facet Al-Sawalha M. Mossa
Al-Sawalha Ayman
author_sort Al-Sawalha M. Mossa
collection DOAJ
description The objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.
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spelling doaj.art-c5d8157b67cf409294473f5069742a522022-12-21T22:39:02ZengDe GruyterOpen Physics2391-54712016-01-0114130431310.1515/phys-2016-0033phys-2016-0033Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive controlAl-Sawalha M. Mossa0Al-Sawalha Ayman1Mathematics Department, Faculty of Science, University of Hail, Kingdom of ArabiaPhysics Department, Faculty of Science, Jerash University, Jerash, JordanThe objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.https://doi.org/10.1515/phys-2016-0033anti-synchronizationadaptive controlfractional order hyperchaosfractional order chaosunknown parameters05.45.-a47.52.+j89.75.-k
spellingShingle Al-Sawalha M. Mossa
Al-Sawalha Ayman
Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
Open Physics
anti-synchronization
adaptive control
fractional order hyperchaos
fractional order chaos
unknown parameters
05.45.-a
47.52.+j
89.75.-k
title Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
title_full Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
title_fullStr Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
title_full_unstemmed Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
title_short Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
title_sort anti synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control
topic anti-synchronization
adaptive control
fractional order hyperchaos
fractional order chaos
unknown parameters
05.45.-a
47.52.+j
89.75.-k
url https://doi.org/10.1515/phys-2016-0033
work_keys_str_mv AT alsawalhammossa antisynchronizationoffractionalorderchaoticandhyperchaoticsystemswithfullyunknownparametersusingmodifiedadaptivecontrol
AT alsawalhaayman antisynchronizationoffractionalorderchaoticandhyperchaoticsystemswithfullyunknownparametersusingmodifiedadaptivecontrol