What question did this study set out to answer?

To examine synchronization in a nonuniform second-order Kuramoto model on an asymmetric network.

On the exponential synchronization for the asymmetric second-order Kuramoto model

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To examine synchronization in a nonuniform second-order Kuramoto model on an asymmetric network.
Analyzed the second-order Kuramoto model with homogeneous dampings on an asymmetric graph.
Developed novel energy functions to control phase and frequency diameters.
Constructed first-order Gronwall-type inequalities for synchronization analysis.
Demonstrated complete frequency synchronization under specified conditions.
Found exponential convergence to a synchronized state with large coupling strength and small inertia.

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The analysis reveals exponential synchronization of a second-order Kuramoto model in an asymmetric graph as coupling strength increases.

Zhu et al. (2026) studied this question.

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