异步网络与事件驱动动态
Asynchronous Networks and Event Driven Dynamics
摘要：
在技术、工程和生物学领域，现实世界的网络经常表现出无法使用光滑动力系统和固定网络拓扑给出的网络模型充分再现的动态特性。异步网络为研究网络动态提供了一个理论和概念框架，其中节点可以相互独立地进化，受到约束，停止，然后重新启动，并且网络不同组件之间的相互作用可能取决于时间，状态和随机效应。这个框架是足够普遍的，涵盖了广泛的应用范围从工程到神经科学。通常，动态是分段光滑的，并且与Filippov系统有关系。在论文的第一部分，我们给出了异步网络的例子，并描述了基本的形式主义和结构。在第二部分中，我们严格地定义了功能异步网络的概念，讨论了动态锁现象，并给出了一个关于一大类功能异步网络动态的时空因子分解的基本结果。
英文摘要：
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks.
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