The mathematical field of bifurcation theory is extended to be applicable to 1-dimensionally resolved systems of nonlinear partial differential equations, aimed at the determination of a certain specific bifurcation. This extension is needed to be able to properly analyze the bifurcations of the radial transport in magnetically confined fusion plasmas. This is of special interest when describing the transition from the low-energy-confinement state to the high-energy-confinement state of the radial transport in fusion plasmas (i.e., the L-H transition), because the nonlinear dynamical behavior during the transition corresponds to the dynamical behavior of a system containing such a specific bifurcation. This bifurcation determines how the three types (sharp, smooth, and oscillating) of observed L-H transitions are organized as function of all the parameters contained in the model.

In more than three decades, a large amount of models and mechanisms have been proposed to describe a very beneficial feature of magnetically confined fusion plasmas: the L-H transition. Bifurcation theory can be used to compare these different models based on their dynamical transition structure. In this paper, we employ bifurcation theory to distinguish two fundamentally different descriptions of the interaction between turbulence levels and sheared flows. The analytic bifurcation analysis characterises the parameter space structure of the transition dynamics. Herewith, in these models three dynamically different types of transitions are characterised, sharp transitions, oscillatory transitions, and smooth transitions. One of the two models has a very robust transition structure and is therefore likely to be more accurate for such a robust phenomenon as the L-H transition. The other model needs more fine-tuning to get non-oscillatory transitions. These conclusions from the analytic bifurcation analysis are confirmed by dedicated numerical simulations, with the newly developed code Bifurcator. [http://dx

Transitions between low and high-confinement (L-H transitions) in magnetically confined plasmas can appear as three qualitatively different types: sharp, smooth, and oscillatory. Bifurcation analysis unravels these possible transition types and how they are situated in parameter space. In this paper the bifurcation analysis is applied to a 1-dimensional model for the radial transport of energy and density near the edge of magnetically confined plasmas. This phenomenological L-H transition model describes the reduction of the turbulent transport by E Â B-flow shear selfconsistently with the evolution of the radial electric field. Therewith, the exact parameter space, including the threshold values of the control parameters, of the possible L-H transitions in the model is determined. Furthermore, a generalised equal area rule is derived to describe the evolution of the transport barrier in space and time self-consistently. Applying this newly developed rule to the model analysed in this paper reveals a naturally occurring transition to an extra wide transport barrier that may correspond to the improved confinement known as the very-high-confinement mode. [http://dx

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