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Daylight plays a major role in the wake/sleep cycle in humans. Indeed, thewake/sleep system stems from biological systems that follow a circadian rhythmdetermined by the light/dark alternation. The oscillations can be modeled bythe higher order non-linearity van der Pol -type equation driven by a term thatmimics the light cycle. In this work noise in the illumination is introduced toinvestigate its effect on the human circadian cycle. It is found that thepresence of noise is detrimental for the sleep/wake rhythm, except for somespecial values for which it may favor regular oscillations. Depending forsystem parameters, noise induces regularities, such as stochastic resonance: ifthe natural light is turned off, it emerges that there is an optimal value ofintensity noise which most deteriorates the regularity of the cycle, it is thephenomenon of anti-coherent resonance. Also, the phenomenon of stochasticresonance occurs: in the presence of the drive of natural light, there is anoptimal noise intensity which improves the evolution of the wake / sleepsystem. However, there is a critical value of the noise beyond which the systembecomes chaotic; indeed, for sufficiently high noise levels (how high dependsupon the parameter of the system), the sleep/wake cycle evolves in a random andunpredictable manner, for whatever parameters of the external light.

Coherence and stochastic resonances in a noisy van der Pol-type circadian pacemaker model driven by light