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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.

    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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  • 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.


  • This article has been cited by:

    1. J. C. Jaime, M. D. Mesa-Álvarez, R. R. Martin, J. A. Betancourt-Mar, G. Cocho, R. Mansilla, J. M. Nieto-Villar, Chronotherapy of cancer: periodic perturbations in vascular growth and metastasis, 2019, 50, 0929-1016, 495, 10.1080/09291016.2018.1465698
    2. Mariano Bizzarri, Oleg Naimark, José Nieto-Villar, Valeria Fedeli, Alessandro Giuliani, Complexity in Biological Organization: Deconstruction (and Subsequent Restating) of Key Concepts, 2020, 22, 1099-4300, 885, 10.3390/e22080885
    3. E. Izquierdo-Kulich, J. M. Nieto-Villar, 2013, Chapter 48, 978-3-642-34069-7, 657, 10.1007/978-3-642-34070-3_48
    4. J.A. Llanos-Pérez, J.A. Betancourt-Mar, G. Cocho, R. Mansilla, José Manuel Nieto-Villar, Phase transitions in tumor growth: III vascular and metastasis behavior, 2016, 462, 03784371, 560, 10.1016/j.physa.2016.06.086
    5. Sheyla Montero, Reynaldo Martin, Ricardo Mansilla, Germinal Cocho, José Manuel Nieto-Villar, 2018, Chapter 8, 978-1-4939-7455-9, 125, 10.1007/978-1-4939-7456-6_8
    6. A. Guerra, D.J. Rodriguez, S. Montero, J.A. Betancourt-Mar, R.R. Martin, E. Silva, M. Bizzarri, G. Cocho, R. Mansilla, J.M. Nieto-Villar, Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition, 2018, 499, 03784371, 208, 10.1016/j.physa.2018.01.040
    7. Mounira Kesmia, Soraya Boughaba, Sabir Jacquir, Control of continuous dynamical systems modeling physiological states, 2020, 136, 09600779, 109805, 10.1016/j.chaos.2020.109805
    8. J. M. Nieto-Villar, R. Mansilla, Longevity, Aging and Cancer: Thermodynamics and Complexity, 2022, 2, 2673-9321, 664, 10.3390/foundations2030045
    9. 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
    10. 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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  • © 2007 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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