Dead Zones Enable Flexible Phase Organization in Coupled Oscillators

Abstract

Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that oscillators remain continuously responsive to inputs and often produce tightly clustered phase distributions. Biological oscillators, however, commonly exhibit phase intervals during which inputs have little or no effect, called ``dead zones." Here, we extend the Kuramoto model by introducing receiver-gated dead zones, in which oscillators transiently ignore incoming signals. Using analytical and numerical approaches, we show that dead zones can reduce synchronization rates, modulate the distribution of phase-locked solutions, and modify the stability of phase-locked states. For identical oscillators, full synchrony remains locally exponentially stable and numerically dominant, although convergence times depend sensitively on the dead-zone width. For heterogeneous oscillators that admit phase-locked solutions when the coupling strength satisfies $K>K^*$, dead zones broaden the long-term phase distributions. Numerical exploration across dead zone widths reveals a transition in which steady phase gaps lose stability, resulting in dead zone-induced phase drifting. Overall, these results identify phase-response dead zones as a biologically plausible mechanism for flexible phase organization beyond classical Kuramoto dynamics.