The emergence of large-scale connectivity and synchronization are crucial to the structure, function and failure of many complex socio-technical networks. Thus, there is great interest in analyzing phase transitions to large-scale connectivity and to global synchronization, including how to enhance or delay the onset. These phenomena are traditionally studied as second-order phase transitions where, at the critical threshold, the order parameter increases rapidly but continuously. In 2009, an extremely abrupt transition was found for a network growth process where links compete for addition in an attempt to delay percolation. This observation of ‘explosive percolation’ was ultimately revealed to be a continuous transition in the thermodynamic limit, yet with very atypical finite-size scaling, and it started a surge of work on explosive phenomena and their consequences. Many related models are now shown to yield discontinuous percolation transitions and even hybrid transitions. Explosive percolation enables many other features such as multiple giant components, modular structures, discrete scale invariance and non-self-averaging, relating to properties found in many real phenomena such as explosive epidemics, electric breakdowns and the emergence of molecular life. Models of explosive synchronization provide an analytic framework for the dynamics of abrupt transitions and reveal the interplay between the distribution in natural frequencies and the network structure, with applications ranging from epileptic seizures to waking from anesthesia. Here we review the vast literature on explosive phenomena in networked systems and synthesize the fundamental connections between models and survey the application areas. We attempt to classify explosive phenomena based on underlying mechanisms and to provide a coherent overview and perspective for future research to address the many vital questions that remained unanswered.

中文翻译：

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复杂网络中的爆炸性现象

大规模连接和同步的出现对于许多复杂的社会技术网络的结构、功能和故障至关重要。因此，人们对分析大规模连接和全局同步的相变非常感兴趣，包括如何增强或延迟开始。这些现象传统上被研究为二阶相变，在临界阈值处，阶参数迅速但连续地增加。2009 年，发现网络增长过程发生了极其突然的转变，其中链接竞争添加以试图延迟渗透。这种对“爆炸性渗透”的观察最终被揭示为热力学极限的连续转变，但具有非常非典型的有限尺寸缩放，它开始了大量关于爆炸现象及其后果的工作。现在显示许多相关模型产生不连续的渗透转变甚至混合转变。爆炸性渗透使许多其他特征成为可能，例如多个巨型组件、模块化结构、离散尺度不变性和非自平均，与许多真实现象中发现的特性有关，例如爆炸性流行病、电击穿和分子生命的出现。爆发同步模型为突然转变的动力学提供了一个分析框架，并揭示了自然频率分布与网络结构之间的相互作用，应用范围从癫痫发作到从麻醉中醒来。在这里，我们回顾了关于网络系统中爆炸现象的大量文献，并综合了模型之间的基本联系并调查了应用领域。我们试图根据潜在机制对爆炸现象进行分类，并为未来的研究提供一个连贯的概述和视角，以解决许多尚未得到解答的重要问题。