2013/06/21 by Cristóbal Quiñinao, Cristobal Quininao, Jonathan Touboul +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #37N25 #82C22 #82C44 #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Neural Networks Stability and Synchronization #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Probability (math.PR) #math-ph #math.MP #math.PR #msc:37N25 #msc:82C22 #msc:82C44 #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1306.5175
openalex publication_date 2013/06/21 · arxiv created 2014/05/15 · arxiv updated 2014/05/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.