Flexible modulation of hybrid feedback loops in competitive biological oscillators.

Biological oscillators control vital rhythmic processes, and their dysregulation is associated with disorders such as cancer, sleep disturbances, and motor deficits. These oscillators often exhibit competitive interactions through mutual inhibition, and their dynamics are regulated by feedback mechanisms: positive feedback enhances synchronization, while negative feedback ensures tunability. However, the role of hybrid (positive-plus-negative) feedback in modulating competitive biological oscillators remains poorly understood. Here, we analyse seven competitive oscillators and demonstrate that hybrid feedback induces two distinct modulation modes: higher-amplitude, lower-frequency oscillations or higher-frequency, lower-amplitude oscillations, depending on hybrid feedback strengths. Furthermore, we show that oscillation tunability hinges on the asymmetry between positive and negative feedback loops. These findings deepen our understanding of oscillation regulation and could guide therapeutic strategies for diseases related to rhythm disorders.