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2007, 4(2): 177-186. doi: 10.3934/mbe.2007.4.177

Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type

Juvencio Alberto Betancourt-Mar 1, and  José Manuel Nieto-Villar 2,

1. 

Laboratorio UNE-SAS, Universidad del Noreste, Prol. Ave. Hidalgo 6315, Tampico, Tams., México, C.P.89337, Mexico
2. 

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

Received  April 2006 Revised  November 2006 Published  February 2007

In this work, the Räossler system is used as a model for chrono- therapy. We applied a periodic perturbation to the y variable to take the Rössler system from a chaotic behavior to a simple periodic one, varying the period and amplitude of forcing. Two types of chaos were considered, spiral and funnel chaos. As a result, the periodical windows reduced their areas as the funnel chaos character increased in the system. Funnel chaos, in this chrono- therapy model, could be considered as a later state of a dynamical disease, more irregular and difficult to suppress.
Keywords: non-linear dynamics, biological rhythm, Rossler system, funnel chaos., chronotherapy, chronobiology, chaotic chemical reactions.
Mathematics Subject Classification: 92C5.
Citation: Juvencio Alberto Betancourt-Mar, José Manuel Nieto-Villar. Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type. Mathematical Biosciences & Engineering, 2007, 4 (2) : 177-186. doi: 10.3934/mbe.2007.4.177
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