Variability and degradation of homeostasis in self-sustained oscillators

Homeostasis is known to be absolutely critical to the sustainability of living organisms. At the heart of homeostasis are various feedback loops, which can control and regulate a system to stay in a most favourable stable state upon the influence of various disturbance. While variability has emerged as a key factor in sustainability, too much variability could however be detrimental. It is thus absolutely crucial to understand the effect of fluctuation in different feedback loops. While modelling technique has achieved a great advancement to understand this issue, too a complicated model however often prevents us from disentangling different many processes. Here, we propose a novel model to gain a key insight into the effect of variability in feedback on self-sustained oscillation. Specifically, by taking into account variation in model parameters for self-excitation and nonlinear damping, corresponding to positive and negative feedback, respectively, we show how fluctuation in positive or negative feedback weakens the efficiency of feedback and affects self-sustained oscillations, possibly leading to a complete breakdown of self-regulation. While results are generic and could be applied to different self-regulating systems (e.g. self-regulation of neuron activity, normal cell growth, etc.), we present a specific application to heart dynamics. In particular, we show that fluctuation in positive feedback can lead to slow heart by either amplitude death or oscillation death pathway while fluctuation in negative feedback can lead to fast heart beat.