Dynamical Analysis Of The Lorenz-84Atmosphere Model With Seasonal Forcing

People can prevent themselves from bad weather via long-term numerical forecast and numerical calculate, hence, it becomes a new area for people exploring. It deals with long-term evolving process and behavior of systems,and the basic theory is the nonlinear dynamics of the compelling dissipation system. We expect to use the theory of the dynamical system to investigate the asymptotic behavior of the nonlinear atmo-sphere dynamical system. Also, we hope to study some specific applications. However, involved researches in this area have just begun and there are a lot of significative works for us to promote further investigation. There are close connections between qualitative theories and numerical computation. The results of the qualitative theory are not only important evidence of the numerical computation, but can also conduce to improve the method of the numerical computation. At the same time, the results of the numerical computation provide abundant material for qualitative theories. Therefore, we hope to get plummy numerical computation results by studying the theories. In this paper, the main achievements are as follows:1. There is a fixed point of the Lorenz-84atmosphere model and people have got corresponding results about the stability of the fixed point. However, the Lorenz-84atmosphere model with seasonal forcing has no fixed points. Hence, we cannot use the Lyapunov method to study the dynamical behaviors of the system. By transfor-mation, the Lorenz-84atmosphere model with seasonal forcing can be changed into a new model,in which there is a fixed point. Thus, the stability of the new system can be investigated and then we can get the dynamical behaviors of the Lorenz-84atmosphere model with seasonal forcing.2. Analyze the dynamical behavior of the Lorenz-84atmosphere model with sea-sonal forcing by numerical analysis while parameter F and G vary in different areas. From the Lyapunov exponent, the curves of the system, the bifurcation map and the Poincare section, the dynamical behavior can be studied. The corresponding numerical results verify the effectiveness of the theoretical analysis.