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While most models of randomly connected networks assume nodes with simpledynamics, nodes in realistic highly connected networks, such as neurons in thebrain, exhibit intrinsic dynamics over multiple timescales. We analyze how thedynamical properties of nodes (such as single neurons) and recurrentconnections interact to shape the effective dynamics in large randomlyconnected networks. A novel dynamical mean-field theory for strongly connectednetworks of multi-dimensional rate units shows that the power spectrum of thenetwork activity in the chaotic phase emerges from a nonlinear sharpening ofthe frequency response function of single units. For the case oftwo-dimensional rate units with strong adaptation, we find that the networkexhibits a state of "resonant chaos", characterized by robust, narrow-bandstochastic oscillations. The coherence of stochastic oscillations is maximal atthe onset of chaos and their correlation time scales with the adaptationtimescale of single units. Surprisingly, the resonance frequency can bepredicted from the properties of isolated units, even in the presence ofheterogeneity in the adaptation parameters. In the presence of theseinternally-generated chaotic fluctuations, the transmission of weak,low-frequency signals is strongly enhanced by adaptation, whereas signaltransmission is not influenced by adaptation in the non-chaotic regime. Ourtheoretical framework can be applied to other mechanisms at the level of singlenodes, such as synaptic filtering, refractoriness or spike synchronization.These results advance our understanding of the interaction between the dynamicsof single units and recurrent connectivity, which is a fundamental step towardthe description of biologically realistic network models in the brain, or, moregenerally, networks of other physical or man-made complex dynamical units.

How single neuron properties shape chaotic dynamics and signal transmission in random neural networks