Genetic programming-based modeling on chaotic time series

One of the difficulties in nonlinear time series analysis is how to reconstruct the system model from the data series. This is mainly due to the dissipation and "butterfly" effect of the chaotic systems. This paper proposes a genetic programming-based modeling (GPM) algorithm for the chaotic time series. In GPM, genetic programming-based techniques are used to search for appropriate model structures in the function space, and the particle swarm optimization (PSO) algorithm is introduced for nonlinear parameter estimation (NPE) on dynamic model structures. In addition, the results of nonlinear time series analysis (NTSA) are integrated into the GPM to improve the modeling quality and the criterion of the established models. The effectiveness of such improvements is proved by modeling the experiments on known chaotic time series.