Insomnia as a Loss of Dynamical Stability

This paper introduces a dynamical systems and control-theoretic framework for understanding insomnia as a problem of stability rather than merely a behavioral or physiological disorder. Sleep is modeled as a stable attractor arising from the coupled dynamics of homeostatic pressure, circadian phase, and arousal. Using a Lyapunov function, we derive conditions under which sleep is maintained, and interpret insomnia as a loss of stability or exit from the basin of attraction. The framework provides a mechanistic explanation of early awakening, formulates interventions as control inputs acting on distinct time scales, and generates testable predictions such as early-warning signals and state-dependent intervention effectiveness. By bridging sleep science, nonlinear dynamics, and control theory, this work offers a principled foundation for personalized and adaptive approaches to insomnia.