Coherence and Stochastic Resonances in a Noisy van der Pol-Type Circadian Pacemaker Model Driven by Light

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.