LYAPROSEN: MATLAB function to calculate Lyapunov exponent
This code uses Rosenstein et al. method with some modifications based on below references. It allow to user select embedding lag( tau) and embedding dimension(m), but if a user cannot give any value to this parameters the code will select automatically this values. For the selection of tau methods of autocorrelation function and minimum mutual information is used in the code. Also two methods namely False Nearest Neighbors and Symplectic Geometry is used for choosing proper value of embedding dimension. -Rosenstein,M. T., J. J. Collins and C. J. De Luca,(1993). A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. -Hai-Feng Liu, Zheng-Hua Dai, Wei-Feng Li, Xin Gong, Zun-Hong Yu(2005) Noise robust estimates of the largest Lyapunov exponent,Physics Letters A 341, 119–127 -Sprott,J. C. (2003). Chaos and Time Series Analysis. Oxford University Press. -Lei, M., Wang Z., Feng Z. A method of embedding dimension estimation based on symplectic geometry, Physics Letters A 303 (2002) 179–189. -Zeng,X., R. Eykholt, and R. A. Pielke (1991)Estimating the Lyapunov-Exponent Spectrum from Short Time Series of Low Precision, Physical Review Letters, Vol. 66, Number 25.
Lyapunov Exponents, Chaos, Time Series, Taylor Expansion, Direct Method, Full Automatic selection code. Minimum mutual Information, Autocorrelation, False nearest neighbors, Symplectic Geometry
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