An application on time series analysis method

Nonlinear time series analysis methods were used to get information about the dynamics of a system. A scalar time series that had been obtained by pneumocardiography from the tracheal airways of a rat which is breathing under anesthesia were studied by nonlinear analysis techniques.First, some basic concepts were reviewed. Then, the techniques that the algorithms originate from were summarized. After that, embedding parameters were determined. In the calculation of time delay, autocorrelation function and mutual information method were used. And in the calculation of embedding dimension, false nearest neighbor method was used. In the embedding space which was reconstructed using these parameters, the attractor of the system was obtained. The dimension of the attractor was calculated. Because of its value is not an integer, it is clear that the attractor has a fractal geometrical structure. Finally, Lyapunov exponents' spectrum was investigated. The presence of positive exponent can be taken as an evidence for the chaotic dynamics. Four different softwares were used to obtain the graphics and numerical results: Dataplore, Nonlinear Dynamics Toolbox (NDT), Visual Recurrence Analysis (VRA) and FD3.