Hopf bifurcation in a mean-field model of spiking neurons

DOI10.1214/21-EJP688zbMath1481.60201arXiv2008.11116OpenAlexW3080442527MaRDI QIDQ2243925

Etienne Tanré, Romain Veltz, Quentin Cormier

Publication date: 11 November 2021

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.11116

zbMATH Keywords

Hopf bifurcationVolterra integral equationlong time behaviormean-field interactionpiecewise deterministic Markov processMcKean-Vlasov SDE

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural biology (92C20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Volterra integral equations (45D05)

Related Items (4)

Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation ⋮ On a Finite-Size Neuronal Population Equation ⋮ Oscillations in a fully connected network of leaky integrate-and-fire neurons with a Poisson spiking mechanism ⋮ Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations

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