Before revision:  We compute the voltage probability distributions and self-consistent firing rates for both types of neurons for finite size spike impacts assuming that inputs are Poissonian. The balanced state exists in a variety of neural network models and its dynamical properties such as chaoticity vary considerably. Our models generalize networks of leaky integrate-and-fire neurons where the dynamics are non-chaotic despite their irregularity. We show that switching the sign of the dissipation of a single neuron renders the entire network dynamics unstable and chaotic as indicated by a positive largest Lyapunov exponent. To further characterize the dynamics we consider the full spectrum of Lyapunov exponents and the related covariant Lyapunov vectors (CLVs) , which indicate the directions in which infinitesimal perturbations grow or shrink with a rate given by the Lyapunov exponents .
After revision:  We compute the voltage probability distributions and self-consistent firing rates for both types of neurons for finite size spike impacts . Further, we compute the full spectrum of Lyapunov exponents and the related covariant Lyapunov vectors (CLVs) , which indicate the directions in which infinitesimal perturbations grow or shrink with a rate given by the Lyapunov exponents .