Dynamical Analysis Of A Low-order Atmospheric Circulation Model

Atmospheric dynamics is an important branch of atmospheric science. In this theory, we regard the atmosphere surrounding the earth as the moving fluid and use the principle and method of fluid mechanics to study the atmospheric motion. The sta-bility of the atmospheric motion is a basic problem in atmospheric dynamics, especially for the nonlinear stability by the action of wave-flow. Now, there are some achievement in this field which has an important application value in long-term weather forecast. In this paper, according to the basic principles of atmospheric motion and existed results of the large-scale atmospheric dynamics, we discuss the dynamical properties of the low-order atmospheric circulation model in great detail. The main achievements are as follows:Firstly, the stability and bifurcation phenomenon of the low-order atmospheric cir-culation model are investigated by the lyapunov method and qualitative theory of differ-ential equations. The global uniform asymptotic stability and existence of limit cycles in the low-order atmospheric circulation model are proved. And the stability condition of the low-order atmospheric circulation model is obtained. When parameters satisfy certain relations, the conditions of the stability and bifurcation of the model are pro-vided. In addition, the Hopf bifurcation is discussed in detail. Besides, the critical bifurcation state is studied based on HKW algorithm.Secondly, the chaotic behavior of the low-order atmospheric circulation model is researched. The Lyapunov exponents, bifurcation diagrams, Poincare section and power spectrum are provided based on the quantitative and qualitative methods. More-over, the bifurcation diagrams and Lyapunov exponent spectrums for every parameter are discussed. Lastly, the parameter interval range of limit cycle and chaotic attractor of every parameter are calculated.The corresponding numerical results coincide with the theoretical method.