Before revision:  The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation time of the dynamics.
After revision:  The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent and the relaxation time of the dynamics.