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September 16, 2025Nonlinearity

Emergent dynamics of the inertial Kuramoto model with frustration on a locally coupled graph

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Emergence of frequency synchronisation is achieved exponentially fast with the constructed energy functions.
First-order dissipative differential inequalities provide the key evidence for the synchronised behaviour of oscillators.
Convex combinations of oscillators are used to develop new techniques for managing phase and frequency dynamics.
Limitations in the second-order gradient flow structure underline the importance of these new energy functions.

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Observational analysis reveals frequency synchronisation in inertial Kuramoto oscillators, suggesting new control mechanisms via energy functions.

Zhu et al. (2025) studied this question.

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Observational analysis reveals frequency synchronisation in inertial Kuramoto oscillators, suggesting new control mechanisms via energy functions.