Theoretical models for chronotherapy: Periodic perturbations in hyperchaos
In this work, a hyperchaotic system was used as a model for chronotherapy. We applied a periodic perturbation to a variable, varying the period and amplitude of forcing. The system, five-dimensional, has until three positive Lyapunov exponents. As a result, we get small periodical windows, but it wa...
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| Format: | Article |
| Language: | English |
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AIMS Press
2010-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.553 |
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| author | Juvencio Alberto Betancourt-Mar Víctor Alfonso Méndez-Guerrero Carlos Hernández-Rodríguez José Manuel Nieto-Villar |
| author_facet | Juvencio Alberto Betancourt-Mar Víctor Alfonso Méndez-Guerrero Carlos Hernández-Rodríguez José Manuel Nieto-Villar |
| author_sort | Juvencio Alberto Betancourt-Mar |
| collection | DOAJ |
| description | In this work, a hyperchaotic system was used as a model for chronotherapy. We applied a periodic perturbation to a variable, varying the period and amplitude of forcing. The system, five-dimensional, has until three positive Lyapunov exponents. As a result, we get small periodical windows, but it was possible to get large areas of hyperchaos of two positive Lyapunov exponents from a chaotic behavior. In this chronotherapy model, chaos could be considered as a dynamical disease, and therapy goal must be to restore the hyperchaotic state. |
| format | Article |
| id | doaj-art-5b3c52c9099146db83439074c40013e0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5b3c52c9099146db83439074c40013e02025-01-24T02:00:43ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-05-017355356010.3934/mbe.2010.7.553Theoretical models for chronotherapy: Periodic perturbations in hyperchaosJuvencio Alberto Betancourt-Mar0Víctor Alfonso Méndez-Guerrero1Carlos Hernández-Rodríguez2José Manuel Nieto-Villar3Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410In this work, a hyperchaotic system was used as a model for chronotherapy. We applied a periodic perturbation to a variable, varying the period and amplitude of forcing. The system, five-dimensional, has until three positive Lyapunov exponents. As a result, we get small periodical windows, but it was possible to get large areas of hyperchaos of two positive Lyapunov exponents from a chaotic behavior. In this chronotherapy model, chaos could be considered as a dynamical disease, and therapy goal must be to restore the hyperchaotic state.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.553generalized r\oo ssler systembiologicalrhythmchronotherapyhyperchaos.chronobiologynon-linear dynamics |
| spellingShingle | Juvencio Alberto Betancourt-Mar Víctor Alfonso Méndez-Guerrero Carlos Hernández-Rodríguez José Manuel Nieto-Villar Theoretical models for chronotherapy: Periodic perturbations in hyperchaos Mathematical Biosciences and Engineering generalized r\oo ssler system biologicalrhythm chronotherapy hyperchaos. chronobiology non-linear dynamics |
| title | Theoretical models for chronotherapy: Periodic perturbations in hyperchaos |
| title_full | Theoretical models for chronotherapy: Periodic perturbations in hyperchaos |
| title_fullStr | Theoretical models for chronotherapy: Periodic perturbations in hyperchaos |
| title_full_unstemmed | Theoretical models for chronotherapy: Periodic perturbations in hyperchaos |
| title_short | Theoretical models for chronotherapy: Periodic perturbations in hyperchaos |
| title_sort | theoretical models for chronotherapy periodic perturbations in hyperchaos |
| topic | generalized r\oo ssler system biologicalrhythm chronotherapy hyperchaos. chronobiology non-linear dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.553 |
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