Collective Dynamics in Complex Networks of Dynamical Systems

该项目的重点是在具有复杂结构的现实网络中建模同步和相干行为。作为一个新兴领域，复杂网络中的同步研究迄今为止还没有看到理论与真实的系统的实际行为之间有足够强的联系。建议的研究的第一个目标是在技术，社会和生物领域的复杂系统的集体动力学的实证分析。这将通过开发三种类型系统的动态数据分析方法来实现：电网，人类社区和生化反应系统。第二个目标是扩展目前的理论框架，分析在这样的系统中的同步和相干动力学。最后的目标是将联合收割机的经验观察和理论发展结合起来，将这些复杂系统建模为简单动态单元的网络。这种方法将用于研究集体动态如何受到底层网络结构和单个动态单元属性的影响。研究电网的同步问题对于评估和减少电压现象在引发大停电事故中的影响具有重要意义。研究人类社会的协调动态有助于制定更有效的战略，以分配服务和资源，评估和管理风险。生物化学反应系统的同步化研究对于我们理解生物体中的大型生物化学网络具有重要意义。计划的研究活动是跨学科的，将涉及培训本科生，包括来自代表性不足的少数民族的学生和一名研究生。外展活动也计划在个人研究咨询和公开讲座的形式在当地高中，使我们的研究成果被呈现给一个大的和不同的公众。

This project focuses on modeling synchronization and coherent behavior in realistic networks with complex structure. As an emerging field, the study of synchronization in complex networks has so far not seen sufficiently strong connections between theory and the actual behavior of real systems. The first objective of the proposed research is the empirical analysis of collective dynamics in complex systems in the technological, social, and biological domains. This will be achieved by developing methods for data analysis of the dynamics of three types of systems: power grids, human communities, and biochemical reaction systems. The second objective is to extend the current theoretical framework for analyzing the synchronized and coherent dynamics in such systems. The final objective is to combine the empirical observations and the theoretical development in the modeling of these complex systems as networks of simple dynamical units. This approach will be used to investigate how the collective dynamics is influenced by the underlying network structure and the properties of the individual dynamical units. The study of synchronization in power grids is important to assess and reduce the influence of voltage phenomena in triggering large blackouts. The study of coherent dynamics in human communities is relevant to help build more efficient strategies for the allocation of services and resources and for the assessment and management of risks. The study of synchronization in biochemical reaction systems is important to advance our understanding of large biochemical networks in living organisms. The planned research activities are interdisciplinary and will involve the training of undergraduate students, including students from under-represented minorities, and one graduate student. Outreach activities are also planned in the form of individual research advising and public lectures at a local high school, allowing our research results to be presented to a large and diverse public.