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2010, 7(3): 553-560. doi: 10.3934/mbe.2010.7.553

Theoretical models for chronotherapy: Periodic perturbations in hyperchaos

Juvencio Alberto Betancourt-Mar 1, , Víctor Alfonso Méndez-Guerrero 1, , Carlos Hernández-Rodríguez 1, and  José Manuel Nieto-Villar 2,

1. 

Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410, Mexico, Mexico, Mexico
2. 

Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba

Received  November 2008 Revised  September 2009 Published  June 2010

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.
Keywords: generalized R\oo ssler system, biological rhythm, Chronotherapy, hyperchaos., chronobiology, non-linear dynamics.
Mathematics Subject Classification: 92C5.
Citation: 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 & Engineering, 2010, 7 (3) : 553-560. doi: 10.3934/mbe.2010.7.553
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