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→与哈密顿系统的联系
== 与哈密顿系统的联系 ==
== 与哈密顿系统的联系 ==
耗散型Kuromoto模型包含在某些具有以下形式的[[哈密顿函数]]的[[保守哈密顿系统]]中：<ref>{{cite journal | last1 = Witthaut | first1 = Dirk | last2 = Timme | first2 = Marc | title = 哈密顿系统中的库拉莫托动力学 | journal = 物理评论E | volume=90 | issue = 3 | pages = 032917 | doi = 10.1103/PhysRevE.90.032917| pmid = 25314514 | year = 2014|arxiv = 1305.1742 |bibcode = 2014PhRvE..90c2917W | s2cid = 7510614 }}</ref>
耗散型Kuromoto模型包含在某些具有以下形式的[[哈密顿函数]]的[[保守哈密顿系统]]中：<ref>{{cite journal | last1 = Witthaut | first1 = Dirk | last2 = Timme | first2 = Marc | title = Kuramoto Dynamics in Hamiltonian Systems | journal = Physical Review E | volume=90 | issue = 3 | pages = 032917 | doi = 10.1103/PhysRevE.90.032917| pmid = 25314514 | year = 2014|arxiv = 1305.1742 |bibcode = 2014PhRvE..90c2917W | s2cid = 7510614 }}</ref>
:<math> \mathcal{H}(q_1,\ldots, q_N, p_1, \ldots, p_N) = \sum_{i = 1}^N \frac{\omega_i}{2} (q_i^2 + p_i^2) + \frac{K}{4N} \sum_{i,j = 1}^{N} (q_i p_j - q_j p_i) ( q_j^2 + p_j^2 - q_i^2 - p_i^2 ) </math>
:<math> \mathcal{H}(q_1,\ldots, q_N, p_1, \ldots, p_N) = \sum_{i = 1}^N \frac{\omega_i}{2} (q_i^2 + p_i^2) + \frac{K}{4N} \sum_{i,j = 1}^{N} (q_i p_j - q_j p_i) ( q_j^2 + p_j^2 - q_i^2 - p_i^2 ) </math>