Dynamical Analysis of the Lorenz-84 Atmospheric Circulation Model

Abstract

The dynamical behaviors of the Lorenz-84 atmospheric circulation model are investigated based on qualitative theory and numerical simulations. The stability and local bifurcation conditions of the Lorenz-84 atmospheric circulation model are obtained. It is also shown that when the bifurcation parameter exceeds a critical value, the Hopf bifurcation occurs in this model. Then, the conditions of the supercritical and subcritical bifurcation are derived through the normal form theory. Finally, the chaotic behavior of the model is also discussed, the bifurcation diagrams and Lyapunov exponents spectrum for the corresponding parameter are obtained, and the parameter interval ranges of limit cycle and chaotic attractor are calculated in further. Especially, a computer-assisted proof of the chaoticity of the model is presented by a topological horseshoe theory.