Chaos, bifurcations and periodic orbits of the Lorenz-Stenflo system

Chaos, bifurcation structures, and periodic orbits of the generalized Lorenz system obtained by Stenflo (1996 Physical Scripta 53 83) for describing nonlinear low-frequency short-wavelength acoustic-gravity waves are investigated. It is shown that both saddle-node and period-doubling bifurcations exist in the domain of Hopf instability, and that forward and backward bifurcations may appear respectively in the rotation and Rayleigh number spaces, but both appear in the Prandtl-number space. Interactive empirical formulas for predicting the higher periodic windows are developed, and orbit characteristics in typical periodic windows are discussed.