Sparse chaos in cortical circuits

Nerve impulses, the currency of information flow in the brain, are generated by an instability of the neuronal membrane potential dynamics. Neuronal circuits exhibit collective chaos that appears essential for learning, memory, sensory processing, and motor control. However, the factors controlling the nature and intensity of collective chaos in neuronal circuits are not well understood. Here we use computational ergodic theory to demonstrate that basic features of nerve impulse generation profoundly affect collective chaos in neuronal circuits. Numerically exact calculations of Lyapunov spectra, Kolmogorov-Sinai-entropy, and upper and lower bounds on attractor dimension show that changes in nerve impulse generation in individual neurons moderately impact information encoding rates but qualitatively transform phase space structure. Specifically, we find a drastic reduction in the number of unstable manifolds, Kolmogorov-Sinai entropy, and attractor dimension. Beyond a critical point, marked by the simultaneous breakdown of the diffusion approximation, a peak in the largest Lyapunov exponent, and a localization transition of the leading covariant Lyapunov vector, networks exhibit sparse chaos: prolonged periods of near stable dynamics interrupted by short bursts of intense chaos. Analysis of large, more realistically structured networks supports the generality of these findings. In cortical circuits, biophysical properties appear tuned to this regime of sparse chaos. Our results reveal a close link between fundamental aspects of single-neuron biophysics and the collective dynamics of cortical circuits, suggesting that nerve impulse generation mechanisms are adapted to enhance circuit controllability and information flow.