2000/01/01 by Wulfram Gerstner · 3 citations
Physics and Astronomy · Neuroscience · Computer Science · #stochastic dynamics and bifurcation #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation
paper · doi:10.1162/089976600300015899
openalex publication_date 2000/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay, and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized"locked"solutions is analyzed.