Boosting of neural circuit chaos at the onset of collective oscillations

Neuronal spiking activity in cortical circuits is often temporally structured by collective rhythms. Rhythmic activity has been hypothesized to regulate temporal coding and to mediate the flexible routing of information flow across the cortex. Spiking neuronal circuits, however, are non-linear systems that, through chaotic dynamics, can amplify insignificant microscopic fluctuations into network-scale response variability. In nonlinear systems in general, rhythmic oscillatory drive can induce chaotic behavior or boost the intensity of chaos. Thus, neuronal oscillations could rather disrupt than facilitate cortical coding functions by flooding the finite population bandwidth with chaotically-boosted noise. Here we tackle a fundamental mathematical challenge to characterize the dynamics on the attractor of effectively delayed network models. We find that delays introduce a transition to collective oscillations, below which ergodic theory measures have a stereotypical dependence on the delay so far only described in scalar systems and low-dimensional maps. We demonstrate that the emergence of internally generated oscillations induces a complete dynamical reconfiguration, by increasing the dimensionality of the chaotic attractor, the speed at which nearby trajectories separate from one another, and the rate at which the network produces entropy. We find that periodic input drive leads to a dramatic increase of chaotic measures at a the resonance frequency of the recurrent network. However, transient oscillatory input only has a moderate role on the collective dynamics. Our results suggest that simple temporal dynamics of the mean activity can have a profound effect on the structure of the spiking patterns and therefore on the information processing capability of neuronal networks.