Choe Chol-Ung, Ri Ji-Song, Kim Ryong-Son
Center for Nonlinear Science, University of Science, Unjong District, Pyongyang, Democratic People's Republic of Korea.
Phys Rev E. 2016 Sep;94(3-1):032205. doi: 10.1103/PhysRevE.94.032205. Epub 2016 Sep 8.
We suggest a site disorder model that describes the population of identical oscillators with quenched random interactions for both the coupling strength and coupling phase. We obtain the reduced equations for the suborder parameters, on the basis of Ott-Antonsen ansatz theory, and present a complete bifurcation analysis of the reduced system. New effects include the appearance of the incoherent chimera and glassy state, both of which are caused by heterogeneity of the coupling phases. In the incoherent chimera state, the system displays an exotic symmetry-breaking behavior in spite of the apparent structural symmetry where the oscillators for both of the two subpopulations are in a frustrated state, while the phase distribution for each subpopulation approaches a steady state that differs from each other. When the incoherent chimera undergoes Hopf bifurcation, the system displays a breathing incoherent chimera. The glassy state that occurs on a surface of three-dimensional parameter space exhibits a continuum of metastable states with zero value of the global order parameter. Explicit formulas are derived for the system's Hopf, saddle-node, and transcritical bifurcation curves, as well as the codimension-2 crossing points, including the Takens-Bogdanov point.
我们提出了一种位点无序模型，该模型描述了具有淬火随机相互作用的相同振子群体，涉及耦合强度和耦合相位。基于奥特 - 安东森假设理论，我们得到了亚序参量的约化方程，并对约化系统进行了完整的分岔分析。新的效应包括非相干奇异态和玻璃态的出现，这两种状态均由耦合相位的不均匀性引起。在非相干奇异态中，尽管系统具有明显的结构对称性，但系统仍表现出奇特的对称破缺行为，其中两个子群体的振子均处于受挫状态，而每个子群体的相位分布趋近于彼此不同的稳态。当非相干奇异态经历霍普夫分岔时，系统会呈现出呼吸型非相干奇异态。出现在三维参数空间表面的玻璃态表现出全局序参量值为零的连续亚稳态。我们推导了系统的霍普夫、鞍结和跨临界分岔曲线以及余维2交叉点（包括塔克恩斯 - 博格达诺夫点）的显式公式。
