Abstract
Daylight plays a major role in the wake/sleep cycle in humans. Indeed, the wake/sleep system stems from biological systems that follow a circadian rhythm determined by the light/dark alternation. The oscillations can be modeled by the higher-order nonlinear van der Pol-type equation driven by a term that mimics the light cycle. In this work, noise in the illumination is introduced to investigate its effect on the human circadian cycle. It is found that the presence of noise is detrimental for the sleep/wake rhythm, except for some special values for which it may favor regular oscillations. Depending on system parameters, noise induces regularities, such as stochastic resonance; if the natural light is turned off, it emerges that there is an optimal value of intensity noise which most deteriorates the regularity of the cycle; it is the phenomenon of anti-coherent resonance. Also, the phenomenon of stochastic resonance occurs; in the presence of natural light and there is an optimal noise intensity which improves the evolution of the wake/sleep system. However, there is a critical value of the noise beyond which the system becomes chaotic; indeed, for sufficiently high noise levels (how high depends upon the parameter of the system), the sleep/wake cycle evolves in a random and unpredictable manner, for whatever parameters of the external light.
Similar content being viewed by others
References
J.C. Dunlap, Molecular bases for circadian clocks. Cell 96, 271–290 (1999)
M.W. Young, S.A. Kay, Time zones: a comparative genetics of Circadian clocks. Nat. Rev. Genet. 2, 702–15 (2001)
D.A. Lombardi, S. Folkard, J.L. Willetts, G.S Smith, Daily sleep, weekly working hours, and risk of work-related injury us national health interview survey (2004–2008). Chronobiol. Int. 27, 1013–1030 (2010)
R.E. Kronauer, D. Forger, M.E. Jewett, Quantifying human circadian pacemaker response to brief, extended, and repeated light stimuli over the phototopic range. J. Biol. Rhythm. 14, 501 (1999)
M.E. Jewett, R.E. Kronauer, Refinement of a limit cycle oscillator model of the effects of light on the human circadian pacemaker. J. Theor. Biol. 192, 455–465 (1998)
R. Yamapi, G. Filatrella, M.A. Aziz-Alaoui, Global stability analysis of birhythmicity in a self-sustained oscillator. Chaos Interdiscip. J. Nonlinear Sci. 20(1), 013114 (2010)
T. Yang, Q. Cao, Noise-induced phenomena in a versatile class of prototype dynamical system with time delay. Nonlinear Dyn. 92, 511–529 (2018)
R. Mbakob Yonkeu, R. Yamapi, G. Filatrella, C. Tchawoua, Effects of a periodic drive and correlated noise on birhythmic van der Pol Systems. Physica A 466, 552–569 (2017)
F.L. Tsafack Tayong, R. Yamapi, G. Filatrella, Entrainment of van der pol-type Cicardian pacemaker to Dayligh cycle. Braz. J. Phys. 51(5), 1416-1427. https://doi.org/10.1007/s13538-021-00948-x
B. Spagnolo, D. Valenti, C. Guarcello, A. Carollo, D. Persano Adorno, S. Spezia, N. Pizzolato, B. Di Paola, Noise-induced effects in nonlinear relaxation of condensed matter systems. Chaos, Solitons & Fractals, 81, 412-424 (2015)
L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223–287 (1998)
R. Yang, A. Song, Int. J. Mod. Phys. B 22, 5365 (2008)
P. Addesso, V. Pierro, G. Filatrella, Commun. Nonlinear Sci. Numer. Simulat. 30, 15 (2016)
S. Fauve, F. Heslot, Stochastic resonance in a bistable system. Physics Letters A. 97A, 5–7 (1983)
A. Bulsara, E.W. Jacobs, T. Zhou, Stochastic resonance in a single neuron model-theory and analog simulation. J. Theor. Biol. 152, 531–555 (1991)
D.S. Leonard, L.E. Reichl, Stochastic resonance in a chemical-reaction. Phys. Rev. E 49, 1734–1737 (1994)
J. Paulsson, M. Ehrenberg, Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks. Phys Rev Lett 84, 5447–5450 (2000)
C. Tao, Q. Liu, B.S. Riddick, W.G. Cullen, J. Reutt-Robey et al., Dynamic interfaces in an organic thin film. Proc. Natl Acad. Sci. USA 105, 16418–16425 (2008)
P. Addesso, V. Pierro, G. Filatrella, Interplay between detection strategies and stochastic resonance properties. Commun. Nonlinear Sci. Numer. Simulat. 30, 15 (2016)
P. Achermann, A. Borberly, Mathematical models of sleep regulation. Front. Biosci. 8, s683 (2003)
R.E. Kronauer, C.A. Czeisler, S.F. Pilato, M.C. Moore-Ede, E.D. Weitzman, Mathematical model of the human circadian system with two interacting oscillators. Am. J. Physiol. Regul. Integr. Comp. Physiol. 242, R3–R17 (1982)
R.E. Kronauer, A quantitative model for the effects of light on the amplitude and phase of the deep circadian pacemaker, based on human data, in Sleep’90. ed. by J.A. Horne (Pontenagel Press, Bochum, Germany, 1990), pp. 306–309
M.E. Jewett, D.B. Forger, R.E. Kronauer, Revised limit cycle oscillator model of human Circadian pacemaker. J. Biol. Rhythms 14, 493–499 (1999)
A.S. Pikovsky, J. Kurths, Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 78(5), 775–778 (1997)
A.A. Zaikin, J. Garcia-Ojalvo, E. Bascones, E. Ullner, J. Kurths, Doublystochastic coherence via noise-induced symmetry in bistable neural models. Phys. Rev. Lett. 90 (3), 030601.1–030601.4 (2003)
F. Chapeau-Blondeau, Stochastic resonance and the benefit of noise in nonlinear systems, in Lecture Notes in Physics, vol. 550 (Springer Berlin ed. 2000), pp. 137–155
D. Middleton, An introduction to statistical communication theory, chap. 1. (McGraw-Hill, New York, 1960)
M. Claning, Kevin, Adittive white Gaussian noise. Radio Receiver Design, Noble Publishing Corporation
F. Ronald, Fox, R. Ian, Gatland, R. Rajarshi, G. Vamuri, Phys. Rev. A. 38, 11 (1988)
N. Corson, Dynamique d’un modle neuronal, Synchronisation et complexit. Thse de doctorat, Universit de Havre (2009)
A.M. Lyapunov, The general problem of the stability of motion. Int. J. Control. 55, 531–773 (1992). This is a translation of a book first published in Russian as Obshchaya zadacha obustoichivosti dvizheniya, Kharkov: Mathematical Society, (1892)
A. Zager, M. Andersen, F. Ruiz, I. Antunes, S. Tufik, Effects of acute and chronic sleep loss on immune modulation of rats. Am. J. Physiol-Reg. I(293), 504 (2007)
R. Yamapi, A. Chamgou, G. Filatrella, P. Woafo, Coherence and stochastic resonance in a birhythmic van der Pol system. Eur. Phys. J. B 90, 153 (2017)
R.L. Stratonovich, Topics in the Theory of Random Noise, vol. 1,2 (Gordon and Breach, 1963)
A. Papoulis, S.U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edn. (McGraw-Hill, Boston, 2002)
F. Mendona, S.S. Mostafa, F. Morgado-Dias, A.G. Ravelo-García, T. Penzela, Review of approaches for sleep quality analysis, special section on advanced information sensing and learning technologies for data-centric smart health applications. IEEE Access 7, 24527–24546 (2019)
L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Stochastic resonance. Rev. Mod. Phys. 70, 223–282 (1998)
R. Yamapi, R. Mbakop Yonkeu, G. Filatrella, C. Tchawoua, Effet on noise correlation on the coherence of a force van der Pol type birythmic sustem. Commun. Nonlinear Sci. Numer. Simulat. 62, 1–17 (2018)
R. Brown, R. Basheer, J. McKenna, R. Strecker, R. McCarley, Control of sleep and wakefulness. Physiol. Rev. 92, 1087 (2012)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tayong, F.L.T., Yamapi, R. & Filatrella, G. Coherence and Stochastic Resonances in a Noisy van der Pol-Type Circadian Pacemaker Model Driven by Light. Braz J Phys 52, 55 (2022). https://doi.org/10.1007/s13538-021-01044-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13538-021-01044-w