  Many neural systems display cascading behavior characterized by uninterrupted
sequences of neuronal firing. This gap precludes an understanding of how
variations in network structure manifest in neural dynamics and either support
or impinge upon information processing. Here, we develop a theoretical
understanding of how network structure supports information processing through
network dynamics, and we validate our theory with empirical data. Using a
generalized spiking model and mathematical tools from linear systems theory,
network control theory, and information theory, we show how network structure
can be designed to temporally extend the propagation and recovery of certain
stimulus patterns. Moreover, we observe cycles as structural and dynamic motifs
that are prevalent in such networks. Broadly, our results demonstrate how
cascading neural networks could contribute to cognitive faculties that require
lasting activation of neuronal patterns, such as working memory or attention.
