Stochastic Kuramoto oscillators with inertia and higher-order interactions

TL;DR

This paper investigates how noise influences synchronization transitions in stochastic second-order Kuramoto oscillators with higher-order interactions, revealing shifts in critical points and changes in transition order.

Contribution

It introduces a perturbation analysis for critical points considering inertia and noise, and explores the transition from first- to second-order synchronization in overdamped systems with higher-order couplings.

Findings

Critical points shift to higher coupling with increased noise.

Transition changes from first-order to second-order as noise increases.

Analytical expression for critical points derived using perturbation analysis.

Abstract

Impact of noise in coupled oscillators with pairwise interactions has been extensively explored. Here, we study stochastic second-order coupled Kuramoto oscillators with higher-order interactions, and show that as noise strength increases the critical points associated with synchronization transitions shift toward higher coupling values. By employing the perturbation analysis, we obtain an expression for the forward critical point as a function of inertia and noise strength. Further, for overdamped systems we show that as noise strength increases, the first-order transition switches to second-order even for higher-order couplings. We include a discussion on nature of critical points obtained through Ott-Antonsen ansatz.