Mean-field Oscillator Games with Application to Thalamocortical Network Dynamics

本奖项的研究目标是探索大种群动态系统中的相变和自组织。方法论工作的重点是动力系统理论和博弈论的交叉。应用的重点是研究大脑丘脑皮质神经元网络的可塑性。这项研究将开发出足够通用的方法，适用于平均场游戏，并可以在各种应用中加以利用。研究方法从理论工具的开发到专门应用到丘脑皮质网络建模。交付成果包括研究耦合振荡器模型中的相变和稳定性的方法和计算工具；这种模型的自适应算法；以及这些工具在丘脑皮层网络降阶建模中的应用；并针对其中的可塑性开发专门的网络适应方案。如果成功，这项研究的结果可以导致我们对在大量动态相互作用的代理中出现的复杂行为的理解取得根本性的进展。对于生物系统，这种方法提供了新的组织原则，以解决长期存在的问题，涉及集体涌现行为在博弈论概念的概括。一个具体的研究成果涉及神经元网络的可塑性（学习）机制。该项目汇集了几项教育举措，以帮助传播方法、成果和跨学科的协同作用。该项目旨在发展和保持本科生对研究的强烈参与，跨学科的推广活动，让工程本科生了解动态和控制在应用中的核心作用，并促进神经科学和工程之间的共生关系。

The research objective of this award is to explore phase transition and self-organization in large population dynamic systems. The thrust of the methodological work is at the intersection of the dynamical systems theory and game theory. The application focus is on investigating plasticity in the thalamocortical neuronal network in brain. The research will develop methods that are general enough to apply for mean-field games and that can be exploited in diverse applications. The research approach progresses from development of theoretical tools to their specialized application to thalamocortical network modeling. Deliverables include methods and computational tools to investigate phase transitions and stability in coupled oscillator models; algorithms for adaptation in such models; and applications of these tools to reduced order modeling of thalamocortical networks; and to development of specialized network adaptation schemes for plasticity therein.If successful, the results of this research can lead to fundamental advances in our understanding of the emergence of complex behavior in a large population of dynamically interacting agents. For biological systems, this methodology offers new organizing principles to address longstanding questions concerning collective emergent behavior in terms of generalizations of game theoretic concepts. A specific research outcome concerns mechanisms for plasticity (learning) in neuronal networks. This project has put together several educational initiatives to help disseminate the methods, outcomes, and the interdisciplinary synergies. This project seeks to develop and maintain strong undergraduate involvement in research, interdisciplinary outreach activities, exposure of the engineering undergraduates to the central role of dynamics and control in applications, and foster symbiotic relationship between neuroscience and engineering.