Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type

Juvencio Alberto Betancourt-Mar; José Manuel Nieto-Villar; Juvencio Alberto Betancourt-Mar; José Manuel Nieto-Villar

doi:10.3934/mbe.2007.4.177

Mathematical Biosciences and Engineering

2007, Volume 4, Issue 2: 177-186. doi: 10.3934/mbe.2007.4.177

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Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type

1.
Laboratorio UNE-SAS, Universidad del Noreste, Prol. Ave. Hidalgo 6315, Tampico, Tams., México, C.P.89337
2.
Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana

Received: 01 April 2006 Accepted: 29 June 2018 Published: 01 February 2007
MSC : 92C50.

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.
- non-linear dynamics,
- biological rhythm,
- Rossler system,
- funnel chaos.,
- chronotherapy,
- chronobiology,
- chaotic chemical reactions
Citation: Juvencio Alberto Betancourt-Mar, José Manuel Nieto-Villar. Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type[J]. Mathematical Biosciences and Engineering, 2007, 4(2): 177-186. doi: 10.3934/mbe.2007.4.177

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Abstract

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.

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