Numerical investigation of the information complexity in Lorenz system based on Shannon entropy

Abstract

To quantify the information embedded in the Lorenz system, the Shannon entropies (also named information entropies) of the convection rate, the horizontal temperature variation, and the vertical temperature variation are calculated under the conditions of different values of the three parameters which are proportional to Prandtl number, Rayleigh number, and the liquid layer dimension respectively. Generalized autoregressive conditional heteroskedasticity models are employed to represent the change of the Shannon entropies with that of the three parameters.