Dynamics in Networks of Spiking Neurons in the Balanced State

The brain processes sensory information about the outside world in large complex networks of neurons which communicate with short electrical pulses called action potentials or spikes. The details of the way information is processed in the brain are not yet well understood. An important boundary condition in this respect is the intrinsic dynamics of neural networks. Yet its quantitative analysis has so far been elusive due to the high complexity of these systems. In this thesis a novel approach is introduced to precisely characterize the collective dynamics and quantify the information preservation and erasure of large networks of spiking neurons. This approach is based on analaytic solutions of the single neuron dynamics and numerically exact simulations, and the calculation of the whole spectrum of Lyapunov exponents. It can be directly applied to arbitrary network topologies and single neuron phase-response curves. This approach is applied to neural networks in the balanced state. The balanced state is the prevailing explanation of the asynchronous irregular activity observed in cortical networks. This irregularity arises due to strongly fluctuating inputs to the neurons that are a result of a dynamic balance of excitation and inhibition. While the emergence and the statistics of the balanced state are rather well understood, its dynamical nature has been discussed controversially. In a comprehensive analysis of exclusively inhibitorily coupled as well as excitatory-inhibitory networks, this thesis demonstrates that neural networks in the balanced state appear to generally exhibit chaotic dynamics. Applying the developed approach to balanced neural networks with different single neuron dynamics and synaptic transmission functions revealed that the action potential generation in the single neuron dynamics plays a key role in determining the strength of chaos. Networks of neurons with low action potential onset rapidness exhibit extensive deterministic chaos. The dynamical entropy production rate in such chaotic networks is strikingly high, such that the sensory information would be overwritten at the same rate as it is provided to the network. Information processing would thus be intrinsically limited to the immediate stimulus response. Increasing the action potential onset rapidness of single neurons decreases the entropy production rate and drives the networks towards the edge of chaos and entangled statistics despite weak pairwise correlations. Because cortical networks were recently found to exhibit much larger action potential onset rapidness than predicted by standard single neuron models, one might speculate that cortical neurons have developed this sharp spike initiation in order to longer preserve the provided sensory input information, and that cortical networks might operate near the edge of chaos. A very large action potential onset rapidness and thus a basically instantaneous spike initiation leads to so-called stable chaos. This formally stable dynamics with respect to infinitesimal perturbations, however, is accompanied by high sensitivity and essentially instantaneous decorrelation of the network microstate after single spike perturbations. The coexistence of stable and extremely unstable dynamics in the same dynamical system draws a picture of a novel exotic phase space structure, namely exponentially separating flux tubes enclosing unique stable trajectories. Summarizing, a novel approach was introduced to thoroughly characterize neural network dynamics and quantify information preservation and erasure. Applying this approach to networks of spiking neurons in the balanced state revealed chaotic dynamics that crucially depends on the details of the action potential generation mechanism of the single neurons