Time after time - circadian clocks through the lens of oscillator theory

Biological systems are fundamentally rhythmic, with oscillations emerging at multiple scales, from intracellular gene circuits to organ-level coordination. Many of these rhythms, including the circadian clock, arise from feedback-driven genetic networks that interact to produce coherent temporal organisation. In this review, we examine the circadian system as a model for understanding the dynamics of coupled biological oscillators. We introduce the core theoretical concepts of delayed feedback, nonlinearity and coupling, and show how these principles govern the emergence of synchronisation, entrainment, and complex dynamics across cellular populations and tissues. Drawing on tools from nonlinear dynamics, we explore how oscillator models help explain robustness, plasticity, and failure modes in circadian systems. Finally, we discuss how this theoretical framework informs experimental design and translational applications in circadian medicine, from optimising drug timing to understanding rhythm disruptions in disease.