Development of an embedded fuzzy-based replication technique for chaotic system

This paper addresses an embedded Fuzzy-based replication technique for chaotic dynamic system. It hybridizes the advantages of Fuzzy Logic that is capable of handling complex, nonlinear and sometimes mathematically intangible dynamic systems and the global modeling capability of embedding phase space. The methodology is based on the fundamental characteristics of chaotic time series, which exhibits some stochastic behavior in time domain and its deterministic behavior can be displayed in the embedding phase space. For a given chaotic time series, an embedding phase space is firstly reconstructed by selecting same appropriate phase space points, the membership function in the fuzzy system will be optimized by using a back-propagation adaptive neural-fuzzy system. The proposed method is demonstrated by an example of Mackey-grass chaotic equation. The repredicted time series are favorably compared to the calculated one.