Theoretical models for chronotherapy: Periodic perturbations in hyperchaos

Juvencio Alberto Betancourt-Mar; Víctor Alfonso Méndez-Guerrero; Carlos Hernández-Rodríguez; José Manuel Nieto-Villar; Juvencio Alberto Betancourt-Mar; Víctor Alfonso Méndez-Guerrero; Carlos Hernández-Rodríguez; José Manuel Nieto-Villar

doi:10.3934/mbe.2010.7.553

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 553-560. doi: 10.3934/mbe.2010.7.553

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Theoretical models for chronotherapy: Periodic perturbations in hyperchaos

1.
Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410
2.
Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana

Received: 01 November 2008 Accepted: 29 June 2018 Published: 01 June 2010
MSC : 92C50.

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.
- generalized R\oo ssler system,
- biological rhythm,
- Chronotherapy,
- hyperchaos.,
- chronobiology,
- non-linear dynamics
Citation: Juvencio Alberto Betancourt-Mar, Víctor Alfonso Méndez-Guerrero, Carlos Hernández-Rodríguez, José Manuel Nieto-Villar. Theoretical models for chronotherapy: Periodic perturbations in hyperchaos[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 553-560. doi: 10.3934/mbe.2010.7.553

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Abstract

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.
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