Flux driven kinetic transport is analysed for deeply trapped ion turbulence with the code GYSELA. The main observation is the existence of a steady state situation with respect to the statistics, in particular the balance between the injected energy and the time averaged energy flowing out through the outer edge boundary layer. The temperature is characterised by a very bursty behaviour with a skewed PDF. Superimposed to these short time scale fluctuations, one finds a regime with a strong increase of the zonal flows and a quenching of the turbulent energy. During this phase of such a predator-prey cycle, the core temperature rapidly increases while the edge temperature gradually decreases. The end of this reduced transport regime is governed by the onset of turbulence that governs large relaxation events, and a strong modification of the zonal flow pattern.