• Lyapunov vectors
• Lyapunov exponents
• ergodic theory
• balanced state
• Neural networks

In the present work the formalism of Ergodic theory, used for the statistical study of complex,
nonlinear dynamical systems of N ≫ 1 dimensions in general, is applied to the time evolution
of large-scale pulse-coupled neural networks in the so-called balanced state. The aim is to
measure the ergodic properties of such systems, consider how they are related to the network
parameters, and finally characterize dynamically the participation of individual network nodes
(the “neurons”) in the collective dynamics.