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Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 553-560. doi: 10.3934/mbe.2010.7.553
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Theoretical models for chronotherapy: Periodic perturbations in hyperchaos

  • 1.
    Mexican Institute of Complex Systems, Tlaxcala 111, Col Unidad Nacional, Cd. Madero, Tampico, Tams., C.P. 89410
  • 2.
    Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana
  • Received: 01 November 2008 Accepted: 29 June 2018 Published: 01 June 2010

  • MSC : 92C50.

  • 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.

    Citation: Juvencio Alberto Betancourt-Mar, Víctor Alfonso Méndez-Guerrero, Carlos Hernández-Rodríguez, José Manuel Nieto-Villar. Theoretical models for chronotherapy: Periodic perturbations in hyperchaos[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 553-560. doi: 10.3934/mbe.2010.7.553

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  • 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.


  • This article has been cited by:

    1. Jian Lin, Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems, 2015, 80, 0924-090X, 209, 10.1007/s11071-014-1861-8
    2. Vasileios Basios, Chris G. Antonopoulos, Hyperchaos & labyrinth chaos: Revisiting Thomas–Rössler systems, 2019, 460, 00225193, 153, 10.1016/j.jtbi.2018.10.025
    3. H. Suárez, A. Guerra, R. Mansilla, J.M. Nieto-Villar, Ferroptosis as a biological Phase transition II: Chronotherapy of avascular and vascular tumor growth, 2023, 0929-1016, 1, 10.1080/09291016.2023.2256522
    4. A. Guerra, J. A. Betancourt-Mar, J. A. Llanos-Pérez, R. Mansilla, J. M. Nieto-Villar, 2024, Chapter 4, 978-1-0716-3576-6, 45, 10.1007/978-1-0716-3577-3_4
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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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