It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks.

了解网络的功能与其结构组织之间的关系是一个基本挑战。自适应动态网络代表了一类广泛的系统，这些系统可以根据其动态状态随时间改变其连接性。此类系统最重要的特征是它们的功能取决于它们的结构，反之亦然。虽然静态网络的特性在过去已经被广泛研究，但自适应网络的研究更具挑战性。此外，自适应动态网络对于各种应用领域都非常重要，特别是对于神经元突触可塑性模型、化学、流行病、生物、运输和社会系统中的自适应网络等。在这篇评论中，我们提供了自适应动态网络的详细描述，