Model Reconstruction Research For Chaos Systems Dynamics

For a practical chaotic system, the adaptive iterative prediction can be performed if an initial dynamical model is obtained. Because the parameters in the initial model are usually unknown or partially known, together with the initial state sensitivity of the chaotic system, the selection of the initial parameter equation is an important problem to deal with. The attractor trajectories of the Dalian temperature and rainfall time series are similar to that of the y and z components in Rossler equation after a careful chaotic characteristics analysis. The paper then applied a technique of dimension expansion so that an initial nonlinear system equation is created by including the system unknown parameters in the identification process. The initial parameters in the equation are determined by referring to the Rossler equations, and then the KF(Kalman Filter) algorithm is used to identify the dynamic characteristics. Both the unknown parameters and the state variable of the system equation are identified, and the adaptive prediction is performed in real time. There are some disadvantages in the application of the Kalman filtering, for example, the inappropriate linearization results in large error when the high order term cannot be ignored. For these points, UKF(Unscented Kalman Filter) is also investigated in this paper for prediction of the Dalian temperature and rainfall time series, since it applied deterministic sampling approach for nonlinear estimation. The simulation results indicate that the UKF method can make a more accurate prediction. Another effort in model reconstruction of chaotic system is emphasized on the local approximation method. The local linear prediction model is applied to the Dalian temperature and rainfall time series. The simulation results show that the method is valuable in the practical application.