The analysis of biomedical time series derived from nonlinear dynamic systems is challenging due to the chaotic nature of these time series. Only few classical parameters can be detected by clinicians to opt the state of patients and fetuses. Though there exist valuable complexity invariants such as multi-fractal parameters, entropies and recurrence plots, they were unsatisfactory in certain cases. To overcome this limitation, we propose in this dissertation new entropy invariants, we contributed to multi-fractal analysis and we developed signal-based (unbiased) recurrence plots and unbiased recurrence descriptors based on the dynamic transitions of time series. Principally, we aim to improve the discrimination between healthy and distressed biomedical systems, particularly fetuses by processing the time series using our techniques. These techniques were either validated on Lorenz systems, logistic maps or fractional Brownian motions which model chaotic and random time series. Then the techniques were applied to real fetus heart rate signals recorded from patients in the third trimester of pregnancy. Statistical measures comprising the relative error, standard deviation, sensitivity, specificity, precision and accuracy were employed to evaluate the performance of detection. Elevated discernment outcomes were realized by the high-order entropy invariants developed. Multi-fractal analysis using a structure function and coarse-graining enhanced the detection of the medical states of the fetuses. Unbiased cross-determinism invariant developed amended the discrimination process. The significance of our techniques lies behind their post-processing codes which could build up cutting-edge portable machines offering advanced discrimination and detection of Intrauterine Growth Restriction prior to fetal death. This work was devoted to Fetal Heart Rates but time series generated by alternative nonlinear dynamic systems should be further considered.