Research Initiation Award: Toward understanding the mechanisms for brain activity patterns by modeling networks of multi time- and amplitude-scale dynamical systems.

研究启动奖为历史悠久的黑人学院和大学的初级和职业生涯中期教师提供支持，这些教师正在建立新的研究计划或重新定向和重建现有的研究计划。预计该奖项有助于进一步提高教师的研究能力和有效性，改善所在机构的研究和教学，并让本科生参与研究经验。授予克拉克·亚特兰大大学(CAU)的奖项可能在许多领域产生更广泛的影响。该项目的目标是促进对具有多时间和多振幅尺度的耦合振子系统网络中集体动力学行为的机制的理解，并通过让非裔美国本科生参与多学科研究活动来加强大学的教与学。对动力学机制的理解对于理解实验观察到的网络振荡至关重要，例如大脑中的神经振荡。这项研究将采用时滞耦合振荡器网络的理论分析和计算建模。它的目的是揭示同步时延正、负耦合的影响；建立混合模式振幅模式起源的一般理论；并开发耦合振荡器的一般网络拓扑，以模拟大脑活动的传播和稳定模式。该项目将通过在课程中嵌入研究项目并培训学生高级分析和计算技能，将应用数学方面的研究和学生培训结合起来。该项目将与佐治亚州立大学合作进行。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. The award to Clark Atlanta University (CAU) has potential broader impacts in a number of areas. The goal of this project is to advance understanding of the mechanisms for collective dynamical behaviors in networks of coupled oscillator systems with multi-time and multi-amplitude scales, and to enhance teaching and learning at the university by involving African American undergraduate students in multidisciplinary research activities. An understanding of the dynamical mechanisms is crucial to make sense of experimentally observed network oscillations, for example, the neural oscillations in the brain. The proposed research will use theoretical analysis and computational modeling of networks of time-delay coupled oscillators. It aims to uncover the effects of time-delayed positive and negative couplings in synchronization; formulate a generalized theory for the origin of mixed-mode amplitude patterns; and develop a general network topology for coupled oscillators to mimic brain activity propagation and stable patterns. The project will integrate research and student training in applied mathematics by embedding research projects in courses and training students in advanced analytical and computational skills. This project will be conducted in collaboration with Georgia State University.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.