Reduced representations of heterogeneous mixed neural networks with synaptic coupling

In the human brain, large-scale neural networks are considered to instantiate the integrative mechanisms underlying higher cognitive, motor, and sensory functions. Computational models of such large-scale networks typically lump thousands of neurons into a functional unit, which serves as the "atom" for the network integration. These atoms display a low dimensional dynamics corresponding to the only type of behavior available for the neurons within the unit, namely, the synchronized regime. Other dynamical features are not part of the unit's repertoire. With this limitation in mind, here we have studied the dynamical behavior of a neural network comprising "all-to-all" synaptically connected excitatory and inhibitory nonidentical neurons. We found that the network exhibits various dynamical characteristics, synchronization being only a particular case. Then we construct a low-dimensional representation of the network dynamics, and we show that this reduced system captures well the main dynamical features of the entire population. Our approach provides an alternate model for a neurocomputational unit of a large-scale network that can account for rich dynamical features of the network at low computational costs.