caa a22 4500 606166556 CHVBK 20210128100658.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10440-014-9945-5 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9945-5 Limits and Dynamics of Randomly Connected Neuronal Networks [Elektronische Daten] [Cristobal Quiñinao, 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 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. Springer Science+Business Media Dordrecht, 2014 Heterogeneous neuronal networks nationallicence Mean-field limits nationallicence Delay differential equations nationallicence Bifurcations nationallicence Quiñinao Cristobal Mathematical Neuroscience Team, CIRB-Collège de France, 11, place Marcelin Berthelot, 75005, Paris, France aut Touboul Jonathan Mathematical Neuroscience Team, CIRB-Collège de France, 11, place Marcelin Berthelot, 75005, Paris, France aut Acta Applicandae Mathematicae Springer Netherlands 136/1(2015-04-01), 167-192 0167-8019 136:1<167 2015 136 10440 https://doi.org/10.1007/s10440-014-9945-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9945-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Quiñinao Cristobal Mathematical Neuroscience Team, CIRB-Collège de France, 11, place Marcelin Berthelot, 75005, Paris, France aut NATIONALLICENCE 700 1- Touboul Jonathan Mathematical Neuroscience Team, CIRB-Collège de France, 11, place Marcelin Berthelot, 75005, Paris, France aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 136/1(2015-04-01), 167-192 0167-8019 136:1<167 2015 136 10440