Propagation of chaos in neural fields

摘要: We consider the problem of limit bio-inspired spatially extended neuronal networks including an infinite number types (space locations), with space-dependent propagation delays modeling neural fields. The chaos property is proved in this setting under mild assumptions on dynamics, valid for most models used neuroscience, a mesoscopic limit, neural-field which we can resolve quite fine structure neuron's activity space and where averaging effects occur. mean-field equations obtained are new type: they take form well-posed infinite-dimensional delayed integro-differential nonlocal term singular spatio-temporal Brownian motion. also show how these intricate be practice to uncover mathematically precise dynamics field particular model exactly reduce deterministic nonlinear equations. These results have several theoretical implications neuroscience review discussion.