Existence theorem and global asymptotical stability for low-dimensional dynamical models of plasma turbulence

Sugama-Horton and Ball-Dewar models are low-dimensional dynamical models that treat interactions between turbulence and emerging global structures from turbulence. These models also demonstrate the transition from low- to high-confinement states of fusion plasmas. We prove global existence theorems and global asymptotical stability of the L-mode solutions of the Sugama-Horton and Ball-Dewar models using the Lyapunov method.