Recently, quantifying the level of the synchrony in non-identical networks has got considerable attention. In the first part of this paper, a new synchronization index for non-identical networks is proposed. Non-identical networks can be categorized into two main types. The first group consists of similar oscillators with miss-match in their parameters, and the second group is organized from completely different oscillators. The synchronizability of the second group of the non-identical networks is more challenging since the amplitude and frequencies of the different oscillators may not be matched. Thus, one way to investigate the limitation of the synchronizability of these networks is to explore the parameter space of their amplitude and frequency. In the second part of this research, the amplitude and frequency of each individual system of the non-identical network are considered as varying parameters and the effect of these parameters on the synchronizability of the network is measured with the propsed index. The results are compared with the conventional indexes, such as the root-mean-square error and phase synchrony with the help of Hilbert transform. The outcomes show that the new proposed synchronization index not only is simple and accurate, but also fast with short computational time. It is not affected by amplitude, phase, or polarity. It can detect the similarity in the fluctuations which is a sign of synchrony in the non-identical networks.

中文翻译：

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新的异同网络同步索引

近来，量化不相同网络中的同步水平已经引起了广泛的关注。在本文的第一部分中，提出了一种新的非相同网络同步索引。不相同的网络可以分为两种主要类型。第一组由参数不匹配的相似振荡器组成，第二组由完全不同的振荡器组成。第二组非相同网络的同步性更具挑战性，因为不同振荡器的幅度和频率可能不匹配。因此，研究这些网络同步性局限性的一种方法是探索其幅度和频率的参数空间。在本研究的第二部分，非相同网络的每个单独系统的振幅和频率都被视为变化的参数，并使用适当的索引来测量这些参数对网络同步性的影响。将结果与常规指标进行比较，例如借助Hilbert变换进行均方根误差和相位同步。结果表明，新提出的同步指标不仅简单，准确，而且计算时间短。它不受幅度，相位或极性的影响。它可以检测到波动中的相似性，这是在不同网络中同步的标志。将结果与常规指标进行比较，例如借助Hilbert变换进行均方根误差和相位同步。结果表明，新提出的同步指标不仅简单，准确，而且计算时间短。它不受幅度，相位或极性的影响。它可以检测到波动中的相似性，这是在不同网络中同步的标志。将结果与常规指标进行比较，例如借助Hilbert变换进行均方根误差和相位同步。结果表明，新提出的同步指标不仅简单，准确，而且计算时间短。它不受幅度，相位或极性的影响。它可以检测到波动中的相似性，这是在不同网络中同步的标志。