# American Institute of Mathematical Sciences

2007, 4(2): 177-186. doi: 10.3934/mbe.2007.4.177

## 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, Mexico 2 Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba

Received  April 2006 Revised  November 2006 Published  February 2007

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. Mathematical Biosciences & Engineering, 2007, 4 (2) : 177-186. doi: 10.3934/mbe.2007.4.177
 [1] Olusola Kolebaje, Ebenezer Bonyah, Lateef Mustapha. The first integral method for two fractional non-linear biological models. Discrete and Continuous Dynamical Systems - S, 2019, 12 (3) : 487-502. doi: 10.3934/dcdss.2019032 [2] Kurt Falk, Marc Kesseböhmer, Tobias Henrik Oertel-Jäger, Jens D. M. Rademacher, Tony Samuel. Preface: Diffusion on fractals and non-linear dynamics. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : i-iv. doi: 10.3934/dcdss.201702i [3] Dorin Ervin Dutkay and Palle E. T. Jorgensen. Wavelet constructions in non-linear dynamics. Electronic Research Announcements, 2005, 11: 21-33. [4] Anugu Sumith Reddy, Amit Apte. Stability of non-linear filter for deterministic dynamics. Foundations of Data Science, 2021, 3 (3) : 647-675. doi: 10.3934/fods.2021025 [5] Ahmad El Hajj, Aya Oussaily. Continuous solution for a non-linear eikonal system. Communications on Pure and Applied Analysis, 2021, 20 (11) : 3795-3823. doi: 10.3934/cpaa.2021131 [6] Wenxiong Chen, Congming Li, Eric S. Wright. On a nonlinear parabolic system-modeling chemical reactions in rivers. Communications on Pure and Applied Analysis, 2005, 4 (4) : 889-899. doi: 10.3934/cpaa.2005.4.889 [7] Faustino Sánchez-Garduño, Philip K. Maini, Judith Pérez-Velázquez. A non-linear degenerate equation for direct aggregation and traveling wave dynamics. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 455-487. doi: 10.3934/dcdsb.2010.13.455 [8] Ahmad El Hajj, Hassan Ibrahim, Vivian Rizik. $BV$ solution for a non-linear Hamilton-Jacobi system. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3273-3293. doi: 10.3934/dcds.2020405 [9] Adrien Blanchet, Philippe Laurençot. Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion. Communications on Pure and Applied Analysis, 2012, 11 (1) : 47-60. doi: 10.3934/cpaa.2012.11.47 [10] Congming Li, Eric S. Wright. Modeling chemical reactions in rivers: A three component reaction. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 377-384. doi: 10.3934/dcds.2001.7.373 [11] Arno F. Münster. Simulation of stationary chemical patterns and waves in ionic reactions. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 35-46. doi: 10.3934/dcdsb.2002.2.35 [12] Marzia Bisi, Maria Groppi, Giampiero Spiga. Flame structure from a kinetic model for chemical reactions. Kinetic and Related Models, 2010, 3 (1) : 17-34. doi: 10.3934/krm.2010.3.17 [13] Marzia Bisi, Giampiero Spiga. On a kinetic BGK model for slow chemical reactions. Kinetic and Related Models, 2011, 4 (1) : 153-167. doi: 10.3934/krm.2011.4.153 [14] Dmitry Dolgopyat. Bouncing balls in non-linear potentials. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 165-182. doi: 10.3934/dcds.2008.22.165 [15] Armin Lechleiter. Explicit characterization of the support of non-linear inclusions. Inverse Problems and Imaging, 2011, 5 (3) : 675-694. doi: 10.3934/ipi.2011.5.675 [16] Denis Serre. Non-linear electromagnetism and special relativity. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 435-454. doi: 10.3934/dcds.2009.23.435 [17] Feng-Yu Wang. Exponential convergence of non-linear monotone SPDEs. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5239-5253. doi: 10.3934/dcds.2015.35.5239 [18] Taqseer Khan, Harindri Chaudhary. Adaptive controllability of microscopic chaos generated in chemical reactor system using anti-synchronization strategy. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 611-620. doi: 10.3934/naco.2021025 [19] Tommi Brander, Joonas Ilmavirta, Manas Kar. Superconductive and insulating inclusions for linear and non-linear conductivity equations. Inverse Problems and Imaging, 2018, 12 (1) : 91-123. doi: 10.3934/ipi.2018004 [20] Jaime Angulo, Carlos Matheus, Didier Pilod. Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system. Communications on Pure and Applied Analysis, 2009, 8 (3) : 815-844. doi: 10.3934/cpaa.2009.8.815

2018 Impact Factor: 1.313