Chaos Phase Space Reconstruction Based on Symbolic Analysis and Multi-Component Conditional Entropy

In the light of the parameters interrelated characteristics in the process of chaos phase space reconstruction, this paper proposed a new way to determine embedding dimension and delay time simultaneously, that is, symbolic analysis-based multi-component conditional entropy method. Conditional entropy was introduced to characterize information increment and served as the measurement of complexity and uncertainty of the system, so that the chaotic attractors could show the most ordered state under the minimum conditional entropy. Symbolic analysis is able to eliminate the interference of some unrelated factors included in system, while reserve the key features of the system information with simple and quick calculation. Furthermore, it could restrain noise effectively and particularly, suitable for the reconstruction of chaotic systems with noise signals. Numerical simulations to typical chaotic system showed that this improving method could obtain the best appropriate embedding dimension and delay time simultaneously, quickly, and accurately. It could reconstruct phase space with high quality and anti-noise features, and provided a new effective way to reconstruct chaos signal.