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.

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