It is shown that ITG turbulence close to the threshold exhibits a long time behaviour, with smaller heat fluxes at later times. This reduction is connected with the slow growth of long wave length zonal flows and, consequently, the numerical dissipation on these flows must be sufficient small. Close to the nonlinear threshold for turbulence generation, a relatively small dissipation can maintain a turbulent state with a sizeable heat flux, through the damping of the zonal flow. Lowering the dissipation causes the turbulence, for temperature gradients close to the threshold, to be subdued. The heat flux then does not go smoothly to zero when the threshold is approached from above. Rather, a finite minimum heat flux is obtained below which no fully developed turbulent state exists. The threshold value of the temperature gradient length at which this finite heat flux is obtained is up to 30% larger compared with the threshold value obtained by extrapolating the heat flux to zero, and the cyclone base case is found to be nonlinearly stable. Transport is subdued when a fully developed staircase structure in the ExB shearing rate (!ExB) is formed, with a shearing rate equal to the growth rate of the most unstable mode (!ExB = ). Just above the threshold, a staircase structure can be observed that, unlike the fully developed staircase associated with the subdued turbulence, has a sizeable radial domain with !ExB < . Although, also in this case !ExB = for a large part of the radial domain, a finite heat flux is obtained through avalanche structures that originate from the !ExB < region, and propagate through the marginally stable regions with !ExB = .