Cristobal Quininao, Jonathan Touboul
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, at different scales, the role of such random architectures in macroscopic activity emerging of such large neuronal networks. We particularly focus on their role in the emergence of periodic solutions.
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http://arxiv.org/abs/1306.5175
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