Cortical neurons exhibit rich dynamics, shaped by the presence of history-dependent biophysical mechanisms such as adaptation over different time scales. On the other hand, cortical circuits are highly recurrent which can result in chaotic network dynamics even if network nodes have simple dynamics . We analyze how the dynamics of nodes (such as single neurons) and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for  networks of multi-dimensional rate units shows that , despite the nonlinear interactions between units, the recurrent network dynamics inherit, in the chaotic phase , the qualitative features of the linear response properties of the single units. For the case of two-dimensional rate units with strong adaptation, we find that the network exhibits a state of "resonant chaos", whose resonance frequency can be predicted from the properties of isolated units . The correlation time of the chaotic network scales with the adaptation timescale of a single unit. Our theory for network analysis can be applied to numerous other mechanisms at the level of single nodes, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between single-neuron mechanisms and recurrent connectivity,  a fundamental step toward the description of biologically realistic network models in the brain, or, more generally, networks of other physical or man-made complex dynamical units.
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales . We analyze how the dynamical properties of nodes (such as single neurons) and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate units shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single units. For the case of two-dimensional rate units with strong adaptation, we find that the network exhibits a state of "resonant chaos", characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated units , even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single nodes, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic network models in the brain, or, more generally, networks of other physical or man-made complex dynamical units.
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Cortical neurons exhibit rich dynamics, shaped by the presence of history-dependent biophysical mechanisms such as adaptation over different time scales. On the other hand, cortical circuits are highly recurrent which can result in chaotic network dynamics even if network nodes have simple dynamics
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales
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dynamics
dynamical properties
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strongly connected
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, despite the nonlinear interactions between units, the recurrent network dynamics inherit,
the power spectrum of the network activity
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, the qualitative features of the linear response properties of the
emerges from a nonlinear sharpening of the frequency response function of
R
whose
characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the
R
. The correlation time of the chaotic network scales with the adaptation timescale of a single unit. Our theory for network analysis
, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework
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numerous
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single-neuron mechanisms
the dynamics of single units
A
which is