The dynamic properties of activity within a neural network are split into three separate regimes, depending on the relative strength of the connectivities between neurons and their tendency to have deminishing activity without external stimulation. In the regime with strong interactions the network exhibits exponentially growing activity and the dynamics are chaotic. This leads to an overstimulation of the network. If the neural interaction is weak, the network activity depletes exponentially in time, i.e. the network does not respond to the external stimulus. In between these two cases lies the critically tuned regime for which the network activity shows a power law decay. This power law is universal for a wide range of different networks as we showed in Randomly coupled differential equations with correlations and Power law decay for systems of randomly coupled differential equations. In this project we will extend the class of models for which this power law decay can be proved and investigate the bondaries of its validity.