2025/12/11 by L. A. Smirnov, Smirnov, L. A., V. O. Munyayev +5
Computer Science · Physics and Astronomy · #Chaos control and synchronization #FOS: Physical sciences #Neural Networks and Reservoir Computing #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2512.10806
openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28
Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order predictive reduction for time-delayed Kuramoto-Daido networks that maps delayed one-dimensional phase dynamics to a delay-free network of two-dimensional rotators. Delay induces effective inertia and triadic interactions, yielding accurate predictions of nontrivial attractors and their collective-state statistics, including splay, cyclops, and chimera states. The reduction reveals a division of roles: inertia organizes higher-dimensional dynamics, whereas triadic terms are crucial for lower-dimensional patterns such as chimeras. Applicable to arbitrary topology, higher harmonics, and intrinsic-frequency heterogeneity, it provides a compact, parameter-explicit reduced model. The same framework also extends to time-delayed amplitude-phase oscillator networks, including swarmalators, yielding analogous reduced equations with emergent inertia and triadic higher-order couplings. This unified and readily deployable description enables systematic prediction and analysis of delay-controlled collective dynamics across oscillator networks.