
In prior work, the Bounded Phase Coherence Principle was proposed as a unifying hypothesis explaining inverted-U stability relationships across physiological domains. This manuscript provides an analytical foundation for that proposal by reframing bounded phase coherence as a dynamical control principle in multiscale biological regulation. Using an Ott–Antonsen mean-field reduction of noisy Kuramoto–Sakaguchi ensembles, we derive closed low-dimensional dynamics for coherence order parameters and connect local recovery rates to Jacobian eigenstructure. A windowed stability functional is introduced that combines recovery, metastability penalties, and complexity rewards, demonstrating how a bounded intermediate operating window of coherence can arise within the synchronized regime, distinct from classical criticality at the synchronization threshold. A simulation-based calibration protocol is outlined, allowing the preferred coherence window to be estimated empirically rather than assumed as a universal setpoint. Version: PreprintRelated work: Expands the theoretical framework introduced in “Bounded Phase Coherence Maximizes Stability in Living Systems” (Zenodo record 18235945).
Complex systems, Physiological regulation, Control theory, Kuramoto model, Nonlinear dynamics, Ott–Antonsen reduction, Dynamical systems theory, Multiplex networks, Synchronization, Multiscale entropy
Complex systems, Physiological regulation, Control theory, Kuramoto model, Nonlinear dynamics, Ott–Antonsen reduction, Dynamical systems theory, Multiplex networks, Synchronization, Multiscale entropy
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