Modeling magnetohydrodynamic turbulence by low-dimensional dynamical systems

This chapter will be focused on the scaling properties of low-frequency magnetohydrodynamic turbulence, as observed both in laboratory and astrophysical plasmas. The presence of anomalous scaling laws are interpreted in terms of deviation of turbulent fluctuations from a Gaussian statistics, that is the presence of intermittency, one of the basic properties of fully developed turbulence. This particular stochastic process can be often investigated through low-order dynamical models, usually called shell model that is able to describe the dynamical behavior of the energy cascade, and can describe the main statistical and dynamical properties of intermittency of real plasma systems.