随机连接神经网络的极限和动力学
Limits and dynamics of randomly connected neuronal networks
摘要：
大脑网络由大量神经元组成，这些神经元通过随机图连接，并在随机延迟后相互作用，这两者都取决于细胞之间的解剖距离。为了理解这些随机结构对这种网络的动力学的作用，我们分析了具有随机相关连接权重和延迟的网络的介观和宏观极限。我们解决了平均和淬火的限制，并显示传播的混沌和收敛到一个复杂的积分分布延迟的McKean-Vlasov方程。然后，我们实例化一个完全可解的模型，说明这种随机架构在新兴的宏观活动中的作用。我们特别关注的作用，连接水平的出现周期性的解决方案。
英文摘要：
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these random architectures on the dynamics of such networks, we analyze the mesoscopic and macroscopic limits of networks with random correlated connectivity weights and delays. We address both averaged and quenched limits, and show propagation of chaos and convergence to a complex integral McKean-Vlasov equations with distributed delays. We then instantiate a completely solvable model illustrating the role of such random architectures in the emerging macroscopic activity. We particularly focus on the role of connectivity levels in the emergence of periodic solutions.
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