Reduction Methodology for Fluctuation Driven Population Dynamics

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these is impossible even slightly deformed due the divergence all moments (cumulants). We solved this problem by introducing a ``pseudocumulants'' expansion. This allows us develop reduction methodology spiking neural networks subject extrinsic and endogenous fluctuations, thus obtaining unified mean-field formulation encompassing quenched dynamical sources disorder.