Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters
The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded ex...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/484039 |
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| _version_ | 1832562506562797568 |
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| author | Xiaomin Tian |
| author_facet | Xiaomin Tian |
| author_sort | Xiaomin Tian |
| collection | DOAJ |
| description | The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme. |
| format | Article |
| id | doaj-art-e6601f72780d41fa9256e462ba821db9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e6601f72780d41fa9256e462ba821db92025-02-03T01:22:31ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/484039484039Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown ParametersXiaomin Tian0School of Automation, Southeast University, Nanjing 210096, ChinaThe complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.http://dx.doi.org/10.1155/2014/484039 |
| spellingShingle | Xiaomin Tian Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters Discrete Dynamics in Nature and Society |
| title | Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters |
| title_full | Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters |
| title_fullStr | Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters |
| title_full_unstemmed | Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters |
| title_short | Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters |
| title_sort | adaptive synchronization between fractional order chaotic real and complex systems with unknown parameters |
| url | http://dx.doi.org/10.1155/2014/484039 |
| work_keys_str_mv | AT xiaomintian adaptivesynchronizationbetweenfractionalorderchaoticrealandcomplexsystemswithunknownparameters |