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A10: Control of stochastic mean-field equations with applications to brain networks
Prof. Dr. Wilhelm Stannat 
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 mathematical literature only quite recently and studied mainly from the theoretical perspective. Their application to neural systems has not yet been investigated.