Selection of minimal length of line in recurrence quantification analysis

A qualitative analysis along with mathematical description was made on the selection of the optimal minimal length of line, lmin, a crucial parameter in the recurrence quantification analysis (RQA). The optimum minimal length of line is defined as a value that enhances the capability of RQA variables (determinism, in this paper) to distinguish between different dynamic states of a system. It was shown that the determinism of the Lorenz time series has a normal distribution. The results indicated that the lowest possible value of the minimal length of line (i.e.,  lmin=2) is the best choice. This value provides the highest differentiation for determinism of the time series obtained from different dynamic states of the Lorenz system. The applicability of the results was verified by examining determinism for monitoring the fluidization hydrodynamics.