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We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic phases, separated by a crossover region characterized by low values of the maximal Lyapunov exponent and participation ratio dimension, but with high values of the Lyapunov dimension that change significantly across the region. Counterintuitively, chaos can be attenuated by either adding noise to strongly modular connectivity or by introducing modularity into random connectivity. Extending the model to include a multilevel, hierarchical connectivity reveals that a loose balance between activities across levels drives the system towards the edge of chaos. 

The neocortex-wide neural activity is organized into distinct networks of areas engaged in different cognitive processes. To elucidate the underlying mechanism of flexible network reconfiguration, we developed connectivity-constrained macaque and human whole-cortex models. In our model, within-area connectivity consists of a mixture of symmetric, asymmetric, and random motifs that give rise to stable (attractor) or transient (sequential) heterogeneous dynamics. Assuming sparse low-rank plus random inter-areal connectivity, we show that our model captures key aspects of the cognitive networks' dynamics and interactions observed experimentally. In particular, the anti-correlation between the default mode network and the dorsal attention network. Communication between networks is shaped by the alignment of long-range communication subspaces with local connectivity motifs and is switchable in a bottom-up salience-dependent routing mechanism. Furthermore, the frontoparietal multiple-demand network displays a coexistence of stable and dynamic coding, suitable for top-down cognitive control. Our work provides a theoretical framework for understanding the dynamic routing in the cortical networks during cognition.