arXiv subjects

Bob W. Rink

Publications and source records attributed to Bob W. Rink.

2 recordsLinked to original sources

arXiv2026

Higher-order phase reduction captures delay-dependent synchronization phenomena in physical oscillator networks

Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks yield explicit insights into their dynamics. However, first-order phase approximations - in which the time delay acts as a phase shift - fail to capture the delay-dependence of synchronization. We develop a systematic approach to derive phase reductions for delay-coupled oscillators to higher order. Beyond first order, already a second-order phase reduction captures delay-induced synchronization as demonstrated in coupled Stuart-Landau oscillators and experiments with delay-coupled electrochemical oscillators. Our results establish a general mechanism by which time delays reshape synchronization phenomena and reveal intrinsic limitations of widely used reduced phase models, with implications for a broad range of oscillator networks.

math.DS↗

arXiv2025

Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation

Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary differential equation coupled with a transport equation, expanding in the coupling strength, and solving the resulting equations order-by-order. This approach yields an approximation of the finite-dimensional phase dynamics to arbitrary order. While in the first-order approximation the time delay acts as a phase shift as expected, the higher-order phase reduction generally displays a less trivial dependence on the delay. In particular, exploiting second-order phase reduction, we prove the existence of a region of bistability in the synchronization dynamics of two delay-coupled Stuart-Landau oscillators.

math.DS↗