Center for Mathematical Science and Advanced Technology (MAT)

Seminar Schedule

[MAT Seminar]

Date:

2026/03/11(Wednesday) 13:00-15:00

Language:

English

Venue:

MAT Theater, 508, IT5F, YES & Zoom (Hybrid)

Speaker:

Riccardo Muolo (RIKEN iTHEMS)

Title:

A parametrization method for higher-order phase reduction: effects of non-pairwise interactions on synchronization dynamics and synchronization engineering

Abstract:

A parametrization method for higher-order phase reduction to understand the effects of non-pairwise interactions on synchronization dynamics. Recent studies have shown that non-pairwise interactions play a crucial role in shaping synchronization dynamics. Such interactions can have different origins. For instance, in systems with physical states xk, xj, xl ∈ ℝ, a non-pairwise coupling may take the form G(xk, xj, xl) = xk xj xl, whereas in phase models with θk, θj, θl ∈ 𝕋, it may appear as g(θk, θj, θl) = sin(θk+θj - 2θl). The link between such physical and phase-level interactions is established through phase reduction for weakly coupled oscillators, generally expressed as an asymptotic expansion in the coupling strength ε. Classical first-order phase reductions, such as the Kuramoto one, capture only pairwise interactions, but higher-order reductions, such as the León and Pazó one, reveal the emergence of non-pairwise terms. These can arise either directly from nonpairwise couplings in the physical variables or at higher orders even when the physical coupling is pairwise. Here, we employ a parametrization-based method for higher-order phase reduction that captures both routes simultaneously by approximating an invariant torus in the full system phase space, providing a unified description of nonpairwise synchronization dynamics. Then, we use such result to "hack" the phase model to obtain the desired dynamics, through a synchronization engineering approach.

©JAMSTEC, www.jamstec.go.jp