耦合振子长程模型中的相变与混沌
Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators
摘要：
研究了仓本模型中同步相变的混沌行为。我们讨论了类似的功能中发现的哈密顿平均场（HMF）模型的关系。我们的数值结果支持这两个模型之间的连接，这可以被认为是一个更一般的阻尼驱动耦合摆动力系统的极限情况下（耗散和保守，分别）。我们还表明，在仓本模型中，相变的形状和最大李雅普诺夫指数行为强烈依赖于固有频率的分布。
英文摘要：
We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection between the two models, which can be considered as limiting cases (dissipative and conservative, respectively) of a more general dynamical system of damped-driven coupled pendula. We also show that, in the Kuramoto model, the shape of the phase transition and the largest Lyapunov exponent behavior are strongly dependent on the distribution of the natural frequencies.
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