Adaptation and Percolation in Complex Networks

复杂网络中的适应和渗透

• 批准号: 0908221
• 负责人: Juan Restrepo
• 金额: $ 24.81万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908221&HistoricalAwards=false
• 关键词: Adaptation; Percolation; Complex; Networks

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Many important dynamical processes take place on networks. Examples include epidemic propagation, genetic regulation, synchronization, information propagation, and many more. Often, these dynamical processes have a modifying effect on the network structure. This project will study the bidirectional interaction of network structure and network processes. As an important and representative case, the synchronization of network-coupled dynamical systems will be studied when network links and oscillator parameters adapt in response to node dynamics. Network and parameter adaptation will be investigated numerically and analytically by developing averaged equations that describe the evolution of the network and oscillator parameters. Possible network fixed points, bifurcations, and attractors in low-dimensional subsets of the space of networks will be studied as a function of various network measures and adaption rules. In a related project, percolation in non-Markovian networks will be studied. The effect of network structure on the percolation threshold has been studied for Markovian networks and for locally tree-like networks. The validity of the Markovian assumption will be tested for various networks arising in applications. Additionally, a way to determine the percolation threshold in non-Markovian networks that are not tree-like will be sought.Network percolation is related to models of epidemic propagation, the propagation of information in a network, or the robustness of networks under attack or random failures. For example, in the epidemic context, the percolation threshold separates networks in which a disease will die out from those in which it will propagate to infect a significant fraction of the population. Our theoretical understanding of how network structure (for example, how people interact with each other during an epidemic) determines this transition is restricted to networks satisfying specific conditions. One of the goals of this project is to directly test whether or not networks found in practice, such as social networks, satisfy them. In addition, existing theoretical tools will be extended to networks that do not satisfy these conditions. Many processes that can be described in terms of networks, such as communication networks of unmanned aerial vehicles, food-chain networks, and neuron networks, do not take place on a static network, but on a network that changes in response to node dynamics. The other part of the project seeks to increase our understanding of how networks change in response to the processes that they mediate, and how they can be described as dynamical objects.

该奖项是根据2009年《美国复苏与再投资法》（公法111-5）资助的。网络上发生了许多重要的动态过程。例子包括流行病的传播，遗传调节，同步，信息传播等等。通常，这些动态过程对网络结构产生修改。该项目将研究网络结构和网络过程的双向相互作用。作为一种重要且具有代表性的情况，当网络链接和振荡器参数适应节点动力学时，将研究网络耦合动力学系统的同步。通过开发描述网络和振荡器参数演化的平均方程，将在数值和分析上对网络和参数适应进行研究。将研究网络空间中的低维基集中可能的网络固定点，分叉和吸引子，这是各种网络测量和适应规则的函数。在一个相关的项目中，将研究非马克维亚网络中的渗透。已经研究了Markovian网络和本地树状网络的网络结构对渗滤阈值的影响。马尔可夫假设的有效性将测试针对应用中产生的各种网络。此外，将要确定非马克维亚网络中不类似树的渗透阈值的方法。网络渗透与流行病的传播模型，网络中信息的传播或攻击下的网络的鲁棒性有关。例如，在流行病的背景下，渗透阈值将疾病将消失的网络分开，而疾病将使疾病传播以感染大量人群的那些网络。我们对网络结构的理论理解（例如，人们如何在流行病期间相互互动）决定了这种过渡仅限于满足特定条件的网络。该项目的目标之一是直接测试在社交网络等实践中发现的网络是否使它们满意。此外，现有的理论工具将扩展到不满足这些条件的网络。可以用网络来描述的许多过程，例如无人机，食品链网络和神经元网络的通信网络，不是在静态网络上进行的，而是在响应节点动力学的响应的网络上进行。该项目的另一部分旨在提高我们对网络如何响应其所述过程以及如何将它们描述为动态对象的理解。