Complexity and delay shape oscillatory transitions in complex networks

Abstract

Oscillation, as a prevalent emergent phenomenon across physical, biological, and ecological systems, is essential for the development and maintenance of many physiological and physical processes. However, the mechanisms through which propagation delays and structural parameters jointly determine the excitation or suppression of oscillatory dynamics remain poorly understood. Here, we show that variations in network complexity, delays, and interaction types provide a parametric route to tuning oscillatory transitions in complex systems. We further demonstrate that delays function as a critical, tunable parameter that complements network complexity in shaping these dynamics. Interestingly, our results reveal that cooperative interactions most effectively promote the emergence of oscillations, outperforming mixed, competitive, and random interaction schemes. Finally, we validate our theoretical predictions through hardware-in-the-loop emulations and demonstrate how network complexity and propagation delays shape oscillatory transitions in an empirically reconstructed complex-network topology.