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

Addresses an embedded fuzzy-based replication technique for chaotic dynamic systems. 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 the embedding phase space. The methodology is based on the fundamental characteristics of a chaotic time series, which exhibits some stochastic behavior in the 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 backpropagation adaptive neural-fuzzy system. The proposed method is demonstrated by an example of Mackey-Glass chaotic equation. The replicated time series compare favorably to the calculated one.