Oscillations, complex spatiotemporal behavior, and information transport in networks of excitatory and inhibitory neurons

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Abstract
Various types of spatiotemporal behavior are described for two-dimensional networks of excitatory and inhibitory neurons with time delayed interactions. It is described how the network behaves as several structural parameters are varied, such as the number of neurons, the connectivity, and the values of synaptic weights. A transition from spatially uniform oscillations to spatiotemporal chaos via intermittentlike behavior is observed. The properties of spatiotemporally chaotic solutions are investigated by evaluating the largest positive Lyapunov exponent and the loss of correlation with distance. Finally, properties of information transport are evaluated during uniform oscillations and spatiotemporal chaos. It is shown that the diffusion coefficient increases significantly in the spatiotemporal phase similar to the increase of transport coefficients at the onset of fluid turbulence. It is proposed that such a property should be seen in other media, such as chemical turbulence or networks of oscillators. The possibility of measuring information transport from appropriate experiments is also discussed.