Synchronization and its slow decay in noisy oscillators with simplicial interactions

Area of Science:

• Complex systems
• Network science
• Nonlinear dynamics

Background:

• Previous studies on oscillator networks with two-simplex interactions revealed phenomena like discontinuous desynchronization and multistability.
• The impact of noise on synchronization in higher-order networks remains poorly understood.

Purpose of the Study:

• To investigate the effect of noise on synchronization in higher-order oscillator networks with generic interactions.
• To understand how different types of simplex interactions influence noise-induced desynchronization and the persistence of synchronized states.

Main Methods:

• Analysis of a higher-order network model incorporating one-simplex and two types of two-simplex interactions with noise.
• Weakly nonlinear analysis to study the emergence of synchronized states.
• Application of Kramers' rate theory for weak noise to derive a dynamical equation for the Kuramoto order parameter.

Main Results:

• Dominant two-simplex interactions lead to noise-induced erosion of synchrony, even with weak noise.
• Synchronized states can persist, with lifetimes increasing exponentially with two-simplex interaction strength.
• Sufficiently strong one-simplex or alternative two-simplex interactions prevent noise erosion, ensuring persistent synchrony.
• Weakly nonlinear analysis shows noise-induced synchronization transitions can be supercritical or subcritical.
• A derived dynamical equation quantifies the time scale of synchronization erosion.

Conclusions:

• Noise significantly impacts synchronization in higher-order networks, with interaction types determining stability.
• Specific network structures and interaction strengths can confer robustness against noise-induced desynchronization.
• Findings provide insights into controlling and designing synchronized oscillator systems in complex networks.