Macroscopic dynamics of noise-driven Izhikevich neural networks

We consider the macroscopic dynamics of all-to-all coupled networks of Izhikevich neurons driven by additive Gaussian white noise. In terms of Lorentz ansatz (LA), the microscopic infinite-sized neuron network is successfully simplified to a macroscopic low-dimensional set of ordinary differential equations using the Fokker–Planck equations and the pseudo-cumulant expansion. This reduction scheme successfully enables us to explore the bifurcation behavior of stochastic dynamics of neuron networks in terms of the mean-field rate equations. With the help of the MatCont toolkit, and the regions of macroscopic collective oscillations of the network induced by noise in the parameter space are identified. The validity of the simplified mean-field equations is verified by comparing the results of the macroscopic description with numerical simulations of stochastic microdynamics of Izhikevich networks. Moreover, we found that noise plays a nontrivial role in modulating and facilitating collective firing dynamics, which has significant physiological and pathological implications. By adjusting the noise intensity, it is possible to effectively disrupt pathological synchronous oscillations and achieve desynchronization of neural clusters.