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

这个项目的主要目标是发展随机平均场方程的控制理论，以及并行的随机反应-扩散系统，以期潜在地应用于大脑状态的控制，用驱动单个神经元内部动力学的弱耦合随机微分方程组的大系统来描述。将特别强调所谓的平均场控制，作为大脑状态的非侵入性外部刺激的数学模型。这种控制只是在最近才在数学文献中被引入，主要是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过。

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.