Finite size effect in Kuramoto oscillators with inertia on simplicial complex

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• The Kuramoto model is a standard framework for studying synchronization in coupled oscillator systems.
• Finite-size effects and inertia are crucial factors influencing collective dynamics but are often neglected in idealized models.

Purpose of the Study:

• To investigate the impact of finite-size effects on the dynamical evolution of the Kuramoto model with inertia and triadic interactions.
• To understand how finite system size drives synchronization and to identify the underlying mechanisms.

Main Methods:

• Analysis of the Kuramoto model with inertia and triadic coupling.
• Comparison of finite-size system behavior with analytical predictions in the thermodynamic limit.
• Identification of the origin of synchronization transitions due to finite size.

Main Results:

• Finite-size fluctuations drive the system towards synchronization at finite coupling, diverging from thermodynamic limit predictions.
• A power-law relationship was found between network size and the critical coupling for synchronization.
• Increased inertia shifts the critical coupling to higher values, counteracting finite-size effects.

Conclusions:

• Finite-size effects play a critical role in inducing synchronization in the Kuramoto model with inertia.
• Inertia acts as a stabilizing factor, opposing the synchronizing influence of finite system size.