A new fractional order hyperchaotic Rabinovich system and its dynamical behaviors |
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| Institution: | 1. Pós-Graduação em Ciências, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil;2. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain;3. Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR, Brazil;4. Instituto de Física, Universidade de São Paulo, 05315-970, São Paulo, SP, Brazil;5. Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Scotland, UK;6. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA |
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| Abstract: | In the paper, the dynamical behaviors of a new fractional order hyperchaotic Rabinovich system are investigated, which include its local stability, hyperchaos, chaotic control and synchronization. Firstly, a new fractional order hyperchaotic Rabinovich system with Caputo derivative is proposed. Then, the hyperchaotic attractors of the commensurate and incommensurate fractional order hyperchaotic Rabinovich system are found. After that, four linear feedback controllers are designed to stabilize this fractional order system Finally, by using the active control method the synchronization is studied between the fractional order hyperchaotic and chaos controlled Rabinovich system In addition, the theoretical predictions are confirmed by numerical simulations. |
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| Keywords: | Fractional dynamics Hyperchaotic Rabinovich system Synchronization Feedback control Active control |
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