Dynamics of a low-order atmospheric circulation chaotic model

In this paper, the dynamics of the Lorenz model of general circulation of the atmosphere is investigated. The global exponential attractive set and positively invariant set are obtained based on well-known Lyapunov stability theory and the function extremum theory for this low-order atmospheric circulation chaotic model. Furthermore, the exponential rate of the trajectories going from the exterior of the attractive set to the interior of the attractive set is also obtained. At last, numerical studies are provided to illustrate the effectiveness of the presented scheme.