Lorenz Chaotic System Parameters Identification Based on a Brief Look at x-state Time Series Only

Parameter identification of Lorenz system based on sampling data only from x- state is investigated in this paper. We use both classic and Least Square based methods to estimate all three parameters. First using Least Square based method, all x- coordinates of fixed points of system obtained. Because of symmetry of two equilibrium points, and trivialness of third, that is zero fixed point, we need two other equations. This paper zooms on properties of spatial domain of x- state time series when trajectory turns in one scroll and doesn’t change it. So sampling must contain unstable oscillations without changing scroll that may occur some times. Frequency of such oscillations and logarithm of two following peaks relation result in zita and damping frequency. Using zita and frequency and also fixed point’s xcoordinate estimation, all three parameters will be determined. None of y and z time series are used. So we don’t need state estimation or full observer.

Keywords:

Lorenz system , fixed point estimation , spatial domain , time series