Time-dependent probability density functions and information geometry in a stochastic prey–predator model of fusion plasmas

A stochastic, prey–predator model of the low to high confinement transition is presented. The model concerns the interaction of a turbulent fluctuation amplitude, zonal flow shear, and the ion density gradient. Delta-correlated noise terms are used to construct Langevin equations for each of the three variables, and a Fokker–Planck equation is subsequently derived. A time-dependent probability distribution function is solved and a number of diagnostic quantities are calculated from it, including the information rate and length. We find the marginal probability distribution functions to be strongly non-Gaussian and frequently multi-modal, showing the coexistence of dithering and H-mode solutions over time. The information rate and length are shown to be useful diagnostics to investigate self-regulation between the variables, particularly the turbulence and zonal flow shear.