Attractors For Fractional Lorenz Systems And Their Application To The Quantification Of Predictability

Although the problem of weather forecasting is very complicated in reality,it is of great significance both in theory and in reality,and it is worthy of our study.In this paper,We first proved the existence of the global attractor of the generalized fractional order Lorenz equation,and found that the global attractor has nothing to do with the parameter b,and the existence of the chaotic attractor is also related to the Rayleigh number ρ.A fourth-order Runge-Kutta was generalized,and numerical simulations were performed to prove that it is faster and more convergent than the predictor-corrector of classical Adams–Bashforth–Moulton method.At the same time,the theoretical data was obtained with the help of the mathematical software Matlab.Finally,by changing the order of the variables of the fractional Lorenz63 model and the parameters r to get different available models,and draw the orbital graphs,the evolution of the global GARs of the vector(x,y,z)and the variables x,y,z and of the root-mean-square error of the models with the time series increase.By analyzing these graphs,it is theoretically inferred that the forecasting conditions applicable to different models are different.