延迟耦合I型可激系统网络的同步
Synchronisation in networks of delay-coupled type-I excitable systems
摘要：
我们使用一个通用的模型为I型兴奋性（称为SNIPER或SNIC模型）来描述在存在非零耦合延迟的网络内的节点的局部动态。利用主稳定性函数的方法，我们研究了网络节点的零滞后同步动力学的稳定性及其对两个耦合参数的依赖性，即耦合强度和延迟时间。与FitzHugh-Nagumo模型（II型兴奋性模型）不同，同步的稳定性取决于耦合强度和延迟时间。这些结果的一个重要含义是，存在复杂的网络，在小世界的方式添加抑制链接可能不仅会导致失去稳定的同步，但也可能restabilizing同步或引入同步和去同步化之间的多个过渡。为了强调我们的研究结果的范围，我们表明，使用斯图尔特-朗道模型，这样的多个过渡不仅发生在可激发系统，但也在振荡的。
英文摘要：
We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.
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