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.
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
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.