Control of stochastic mean-field equations with applications to brain networks (A10*)

随机平均场方程的控制及其在脑网络中的应用 (A10*)

• 批准号: 413877837
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/413877837?language=en
• 关键词: Control; stochastic; mean; field; equations

The main goal of this project is to develop the control theory of stochastic mean-field equations, and in parallel, stochastic reaction-diffusion systems, with a view towards potential applications to the control of brain states, described in terms of large systems of weakly coupled stochastic differential equations driving the internal dynamics of single neurons. Special emphasize will be laid on so called mean-field controls as mathematical models for non-invasive external stimulations of brain states. Such controls have been introduced in the math-ematical literature only quite recently and studied mainly from the theoretical perspective. Their application to neural systems has not yet been investigated.

这个项目的主要目标是发展随机平均场方程的控制理论，并在并行，随机反应扩散系统，着眼于潜在的应用程序控制大脑状态，描述在大系统的弱耦合随机微分方程驱动的内部动态的单个神经元。将特别强调所谓的平均场控制，作为大脑状态非侵入性外部刺激的数学模型。这种控制只是最近才在数学文献中被介绍，并且主要从理论的角度进行研究。它们在神经系统中的应用尚未被研究。