Giannuzzi F, Marinazzo D, Nardulli G, Pellicoro M, Stramaglia S
Dipartimento Interateneo di Fisica, Università di Bari, Bari, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 1):051104. doi: 10.1103/PhysRevE.75.051104. Epub 2007 May 3.
We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions and mechanical systems. We let the global coupling k be a function of the Kuramoto order parameter r through an exponent z such that z=1 corresponds to the standard Winfree model, z<1 strengthens the coupling at low r (low amount of synchronization), and at z>1 , the coupling is weakened for low r . Using both analytical and numerical approaches, we find that z controls the size of the incoherent phase region and that one may make the incoherent behavior less typical by choosing z<1 . We also find that the original Winfree model is a rather special case; indeed, the partial locked behavior disappears for z>1 . At fixed k and varying gamma , the stability boundary of the locked phase corresponds to a transition that is continuous for z<1 and first order for z>1 . This change in the nature of the transition is in accordance with a previous study of a similarly modified Kuramoto model.
我们研究了一个广义Winfree模型的相图。这种修改使得耦合依赖于同步振子的比例，这种情况在一些关于耦合约瑟夫森结和机械系统的实验中已经被注意到。我们通过指数z使全局耦合k成为Kuramoto序参量r的函数，其中z = 1对应于标准的Winfree模型，z < 1在低r（低同步量）时增强耦合，而在z > 1时，低r时耦合减弱。通过使用解析和数值方法，我们发现z控制着非相干相区域的大小，并且通过选择z < 1可以使非相干行为不那么典型。我们还发现原始的Winfree模型是一个相当特殊的情况；实际上，对于z > 1，部分锁定行为消失。在固定k并改变γ时，锁定相的稳定性边界对应于一个转变，该转变对于z < 1是连续的，对于z > 1是一阶的。这种转变性质的变化与之前对一个类似修改的Kuramoto模型的研究一致。
