论文标题
库拉莫托平均野外游戏中的同步
Synchronization in a Kuramoto Mean Field Game
论文作者
论文摘要
在无限的地平线平均野外游戏的环境中研究了古典库拉莫托模型。该系统显示出表现出同步和相变。均匀分布的稳定性证明了低于相互作用参数的临界值的不一致。高于此价值，游戏会分叉并发展自组织的时间同质纳什均衡。随着相互作用变得更强，这些固定溶液变得完全同步。结果通过非线性部分微分方程，粘度解决方案，随机最佳控制和随机过程的技术证明了结果。
The classical Kuramoto model is studied in the setting of an infinite horizon mean field game. The system is shown to exhibit both synchronization and phase transition. Incoherence below a critical value of the interaction parameter is demonstrated by the stability of the uniform distribution. Above this value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions become stronger, these stationary solutions become fully synchronized. Results are proved by an amalgam of techniques from nonlinear partial differential equations, viscosity solutions, stochastic optimal control and stochastic processes.
