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August 12, 2025Chaos An Interdisciplinary Journal of Nonlinear Science

Stability of uniformly incoherent state in the D-dimensional generalized Kuramoto model

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Authors

XZXiaoting ZhangSouth China Normal UniversityWZWei ZouHuazhong University of Science and Technology

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Implication

Theoretical analysis reveals stability criteria for incoherent states in high-dimensional systems, indicating phase transition potential.

Key Points

  • The critical coupling strength for the instability of the uniformly incoherent state is confirmed to be zero for all odd dimensions D≥3.
  • Stability information about complete incoherence can be derived from a reduced system using the Ott–Antonsen ansatz.
  • The characteristic equation simplifies for both even and odd dimensions, aiding in stability assessments of large systems.
  • This analysis forms a theoretical foundation for understanding phase transitions in interacting high-dimensional agents.

Cite This Study

Zhang et al. (2025) studied this question.

synapsesocial.com/papers/68a3633d0a429f7973329e53https://doi.org/10.1063/5.0285606
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