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

TL;DR

This paper investigates how noise in light affects a mathematical model of human circadian rhythms, revealing phenomena like stochastic and anti-coherent resonance, and identifying noise levels that can either improve or disrupt sleep/wake cycles.

Contribution

It introduces noise into a van der Pol-type circadian model and analyzes its effects, uncovering resonance phenomena and thresholds for chaos.

Findings

Noise can induce regular oscillations under certain conditions.

Optimal noise levels can enhance the regularity of the sleep/wake cycle.

High noise levels lead to chaotic and unpredictable rhythms.

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 non-linearity 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 for 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 the drive of natural light, 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.