Generalized complex Lorenz system for plasmas and the transition to turbulence

A generalized complex Lorenz system is derived for toroidal plasmas. The 26-dimensional set is found to have far-reaching similarities with the complex Lorenz system including unmodified asymptotic conservation relations and limit-cycle frequency. The complex Lorenz system is also found to dominate close to the stability boundary. An asymptotic analytical solution including 11 modes has been obtained which gives a good approximation of the full system in weakly unstable cases. For higher values of the Prandtl number the limit cycle is found to bifurcate to doubly periodic or chaotic motion.