Study on entrainment and chaos in coupled qualitatively different oscillators

目前的研究主要致力于阐明在全球和扩散耦合振子的非活性元素（阻尼振子）的比例增加的效果的主题。主要结果如下：1.老化转变以耦合Stuart-Landau（SL）振子和耦合Roessler系统为例，发现当耦合强度K大于某一阈值时，系统在非活性元素比p小于1时停止振荡：p<1.2.老化转变时的普适标度引入系统质心的振荡幅度作为老化转变的序参量，3.去极化角-有源振荡器同步的破坏-发现有源振荡器在（K，p）相图的角状区域中去极化并形成团簇，只要振荡器的非等时性足够强。4.扩散诱导的不均匀性--摆动机制--确定了增加K值导致去极化喇叭中系统不均匀性增强的机制。5.测量相序参数的实验方法与弗吉尼亚大学的一个研究小组合作，提出了一种仅用一个宏观量的数据测量大量振子的相序参数的方法。这一方法有待推广到老化系统。

Present research was mainly devoted to the subject of elucidating the effect of increasing the ratio of inactive elements (damped oscillators) in globally and diffusively coupled oscillators. Main results are as follows :1.Aging transitionWe found by taking coupled Stuart-Landau(SL) oscillators and coupled Roessler systems as examples that when the coupling strength K is larger than a threshold value, the system stops oscillation at a value of the ratio of inactive elements, p, which is less than one : p<1.2.Universal scaling at the aging transitionOscillation amplitude of the centroid of the system, which was introduced as an order parameter of the aging transition, was shown to obey universal scaling laws at the transition.3.Desynchronization horn - violation of the synchronization of active oscillators -Active oscillators were found to desynchronize and form clusters in a horn-like region of the (K,p) phase diagram, provided that the nonisochronicity of oscillators is sufficiently strong. This phenomenon was analyzed in detail for coupled SL oscillators.4.Diffusion-induced inhomogeneity - Swing-by mechanism -The mechanism was identified by which increasing the value of K leads to an enhancement of the system's inhomogeneity in the desynchronization horn. Moreover, a theory was presented to predict for what value of K the system becomes most inhomogeneous.5.An experimental method to measure phase order parametersIn collaboration with a Virginia university group, a method was proposed to measure phase order parameters of a large population of oscillators using only data of one macroscopic quantitiy. This method remains to be extended to aged systems.