Open AccessTheoretical models for chronotherapy: Periodic perturbations in hyperchaos
Author(s) -
Juvencio Alberto Betancourt-Mar,
Víctor Alfonso Méndez-Guerrero,
Carlos Hernández Rodríguez,
J.M. Nieto-Villar
Publication year - 2010
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2010.7.553
Subject(s) - chronotherapy (sleep phase) , lyapunov exponent , control theory (sociology) , chaotic , perturbation (astronomy) , mathematics , forcing (mathematics) , lyapunov function , attractor , statistical physics , physics , computer science , mathematical analysis , nonlinear system , artificial intelligence , control (management) , quantum mechanics , astronomy , morning
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.