Phase Space Reconstruction Of Multi-Input Complex System And Its Applation

Through analyzing the variables’time series from complex system, reconstruct a phase space that can clearly show the evolution tracks of the variables, then determine the input vector including the composition of variables and their delayed states. Lastly, build evolution or predication model of the system. This reconstruction is the basis of revealing dynamic law for complex system. The paper concentrates on phase space reconstruction of multivariable system and its application. As follows:1) The selection of multi-input variables participated in reconstruction. Considering the nonlinearity of the system, a concept of nonlinear correlation degree is introduced to compute the nonlinear correlation between output variable and other variables. Compontents of input vector are defined. Then use the popular C-C method to construct an intial phase space based on the selected variables by computing the embedding dimension and the embedding delay of each variable construct an input vector composed by different delay time states of multi variables. The simulated results show that combination of variables which have large correlation degree to output can be used in reconstruction. The information contained in reconstructed phase space is beneficial to make prediction. Therefore a new idea is provided for the selection of input vectors in reconstructing phase space.2) Demention reduction of the high dimensional input phase space. Based on (1), there are some problems existed in the intinal input vector, such as high demension reduction, redundant information and so on. Using the variables’delay reconstruction at time t as the input vector of ICA model, the independent component are extracted, which can reduce the input dimension as well as assure the containing of the effective information. This will reduce the difficulty of modeling and analysis. Apply the procedure to a typical complex system—Rossler equation. Simulation results show that the tracks in worked phase space after demention reduction has clear orbit. In multivariable prediction, the proposed method can reduce the calculation difficulty and improve prediction accuracy.