Diffusively Coupled Networks: Synchronization, De-Synchronization, and Structure

该项目将为空间分布网络开发新的设计和分析技术，这些网络表现出生物分子网络和多代理系统中常见的扩散耦合结构。这一发展的第一步将是解开代理动力学的结构特性及其相互连接，产生规定的空间行为，如同步或模式的形成。第二步将是通过架构决策来增强所需的属性。开发的技术将服务于生物分子网络和多代理系统，以及其他具有类似结构的应用程序。建议的第一部分提出了一种新技术，以确定哪些条件保证扩散耦合网络中的同步行为。除了离散代理网络，这种技术是适用于连续反应扩散模型，同步意味着空间均匀性。一个关键的研究任务将是开发新的系统增益概念，量化的空间模型变化量所造成的不均匀性的量，并将结果应用到振荡器网络和生物分子信号级联。第二部分旨在诱导理想形式的去同步以产生空间模式，这是合成生物学中的突出问题之一。它建议采用系统理论的概念来设计新的基因网络，这些网络适合于合成实现，并在规定的空间模式中表现出扩散驱动的不稳定性，从而导致这些模式主导的基因表达模式。提案中确定并详细说明了一种这样的拓扑结构。第三部分假定扩散驱动的不稳定性和非最小相代理动力学之间的联系，并证明这种不稳定性的一种形式可以发生在多代理系统。然后，它提出了调查的限制，可实现的同步性能所施加的非最小相位代理，并减轻由此产生的设计权衡与重新分配的节点和链路的权重，通过凸optimization.Broader影响PI将继续纳入研究生课程的研究材料。 此外，他将介绍从这个项目中选择的主题到两个本科课程。 PI领导招聘和指导其部门中代表性不足的研究生，并将尽一切努力为拟议项目招聘一名女性或少数民族研究生研究员。

ObjectiveThis project will develop novel design and analysis techniques for spatially distributed networks that exhibit a diffusive coupling structure, common in biomolecular networks and multi-agent systems. The first step in this development will be to unravel structural properties of agent dynamics and their interconnection that yield prescribed spatial behaviors, such as synchronization or pattern formation. The second step will be to enhance the desirable properties via architectural decisions. The techniques to be developed will serve biomolecular networks and multi-agent systems, as well as other applications that possess similar structuresIntellectual MeritPart One of the proposal sets forth a new technique to determine which conditions guarantee synchronous behavior in diffusively coupled networks. In addition to networks of discrete agents, this technique is applicable to continuous reaction-diffusion models where synchrony means spatial homogeneity. A key research task will be to develop new system gain concepts that quantify the amount of inhomogeneity caused by the amount of spatial model variation, and to apply the results to oscillator networks and biomolecular signaling cascades. Part Two aims to induce desirable forms of de-synchronization to generate spatial patterns, which is one of the outstanding problems in synthetic biology. It proposes to employ systemtheoretic concepts to design new gene networks that are amenable to synthetic implementation and that exhibit diffusion-driven instability in prescribed spatial modes, thus leading to gene expression patterns dominated by these modes. One such topology is identified and detailed in the proposal. Part Three posits a connection between diffusion-driven instability and nonminimum-phase agent dynamics, and demonstrates that a form of this instability can occur in multi-agent systems. It then proposes to investigate the limits of achievable synchronization performance imposed by nonminimum-phase agents, and to mitigate the resulting design tradeoffs with a re-allocation of node and link weights to be performed via convex optimization.Broader Impact The PI will continue incorporating research material into graduate courses. In addition, he will introduce selected topics from this project into two undergraduate courses. The PI leads recruitment and mentoring of underrepresented graduate students in his department, and will make every effort to recruit a female or minority graduate student researcher for the proposed project.