Numerical bifurcation and Hopf continuation of Lorenz–Stenflo system

Abstract

A graphical overview of the bifurcation structures and their behaviour of the Lorenz–Stenflo system (Stenflo 1996 Phys. Scr. 53 83) for describing nonlinear low-periodic short-wavelength acoustic gravity waves are investigated. We utilize the MATCONT2.5.1 package to analyse the detailed bifurcation scenarios as the physical and control parameters are varied. The variety of patterns revealed here has not been studied before. Using forward and backward bifurcations, the Hopf bifurcation and their continuation curves of the system are presented in the rotation and Rayleigh number plane, Prandtl number and rotation plane, and also in the rotation and geometric parameter plane. These bifurcation phenomena and their behaviour may be useful for better prediction of existence and stability of large-scale quasi-stationary structures amid chaotic motion in the atmosphere.