Forward and backward processes associated with the low-to-high (L-H) transition in magnetically confined fusion plasmas are investigated by using a time-dependent probability density function (PDF) approach and information length diagnostics. Our model is based on the extension of the deterministic prey–predator-type model [Kim and Diamond, Phys. Rev. Lett. 90, 185006 (2003)] to a stochastic model by including two independent, short-correlated Gaussian noises. The “forward” process consists of ramping up the input power linearly in time so that zonal flows self-regulate with turbulence after their initial growth from turbulence. The “backward” process ramps the power down again, by starting at time t=t* when the input power is switched to Q(t)=Q(2t*t) for t>t*, linearly decreasing with time until t=2t*. Using three choices for Q(t), with differing ramping rates, the time-dependent PDFs are calculated by numerically solving the appropriate Fokker–Planck equation, and several statistical measures including the information length for the forward and backward processes are investigated. The information lengths Lx(t) and Lv(t) for turbulence and zonal flows, respectively, are path-dependent dimensionless numbers, representing the total number of statistically different states that turbulence and zonal flows evolve through in time t. In particular, PDFs are shown to be strongly non-Gaussian with convoluted structures and multiple peaks, with intermittency in zonal flows playing a key role in turbulence regulation. The stark difference between the forward and backward processes is captured by time-dependent PDFs of turbulence and zonal flows and the corresponding information length diagnostics. The latter are shown to give us a useful insight into understanding the correlation and self-regulation, and transition to the self-regulatory dithering phase.

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