Identifying steady state in the network dynamics of spiking neural networks

Abstract

Analysis of the dynamics of complex networks can provide valuable information. For example, the dynamics can be used to characterize and differentiate between different network inputs and configurations. However, without quantitatively delineating the network's dynamic regimes, analysis of the network's dynamics is based on heuristics and qualitative signatures of transient or steady-state regimes. This is not ideal because interesting phenomena can occur during the transient regime, steady-state regime, or at the transition between the two dynamic regimes. Moreover, for simulated and observed systems, precise knowledge of the network's dynamical regime is imperative when considering metrics on minimal mathematical descriptions of the dynamics, otherwise either too much or too little data is analyzed. Here, we develop quantitative methods to ascertain the starting point and period of steady-state network activity. Using the precise knowledge of the network's dynamic regimes, we build minimal representations of the network dynamics that form the basis for future work. We show applications of our techniques on idealized signals and on the dynamics of a biologically inspired spiking neural network.