The biological signals represent patterns of change in the rhythms of biological system that provides a complementary way to study the dynamics of these systems. These signals carry information that is vitally important for understanding of underlying dynamics of living systems. The availability of large and complex data sets and available computational tools allows a complimentary way to develop our understanding about the functioning of the physiological systems, their structures and dynamics. Various innovative approaches such as time-frequency and complexity analysis measures and their computational tools have been developed in recent years to get insight into a wide range of physiological and pathological conditions. These approaches and computation tools are applicable in wide range of disciplines to study the dynamics of biological systems. However, this research work is focused on studying the dynamical fluctuations of EEG signals for detecting epileptic seizure, differentiating alcoholic and non-alcoholic subjects as well as for quantifying the dynamics of healthy subjects with eye open and eye-closed during resting state. The research reported in this dissertation is based on methodological approaches used to quantify the dynamical fluctuations of neurophysiological systems. The first direction of the research was to use time-frequency representation (TFR) techniques such as spatial wavelet phase coherence and coupling to analyze the dynamics of EEG signals in different frequency bands in the form of topographic maps. The distribution of power in different frequency bands was computed. The findings indicated that the power in delta frequency band is mainly distributed in prefrontal and occipital regions, the power in theta band in fronto-occipital regions, power in alpha in posterior and extended to anterior, power in beta in posterior, prefrontal regions and power in gamma was dominant in prefrontal and occipital regions. All the frequency bands were involved in different activities in one way or other, however alpha band power revealed dominant anterior-posterior activity where the eye-closed coherence was higher than eye open coherence. The growing experimental evidences suggest that neural processing relies on the interaction between frequency bands and there is cross frequency coupling (CFC) present in the brain signals. Therefore, understanding of CFC patterns can be valuable tool for diagnosing and treating various neurological disorders. The phase-phase CFC on multichannel electroencephalographic (EEG) signals with EC and EO during resting state was computed to investigate which brain regions are affected by phase modulation of low frequency bands. Coupling in different frequency bands was estimated using dynamic Bayesian inference approach which can effectively detect the phase connectivity subject to the noise within a network of time varying coupled phase oscillators. Coupling was bidirectional in both EC and EO and was relatively higher in EC condition. The self, direct and common coupling scheme showed strong coupling in delta-alpha to alpha (?,?→?) and theta-alpha to alpha (?,?→?) bands. However, moderate couplings were found in theta-gamma to gamma (?,?→?), alpha-gamma to gamma (?,?→?) and delta-gamma to gamma ?,?→?) bands. The second direction was to use scale based complexity analysis technique including Multiscale Sample Entropy (MSE) and Multiscale Permutation Entropy (MPE) to quantify the dynamics of neurophysiological systems using EEG signals. The recent research evidence suggests that complexity of biological system is multiscaled and hierarchical. The findings revealed that Multiscale Permutation Entropy (MPE) gave statistically significant results and separation to distinguish the alcoholic from non-alcoholic subjects, EEG motor movement with baseline EO and EC at all selected electrodes. Moreover, Multiscale Sample Entropy (MSE) was applied to distinguish EEG with epileptic seizures and healthy subjects. MSE gives statistically high significant results to distinguish the epileptic (with and without seizures) subjects with healthy subjects at all temporal scales. The third direction was to quantifying the dynamics of physiological systems using Threshold based Symbolic Time series. The normalized corrected Shannon entropy (NCSE) was computed for EEG signals during EO and EC resting states to quantify the dynamics of these systems at a range of thresholds. The results revealed significant differences between healthy and epileptic seizures subjects and EEG signals with EC and EO during resting states. The symbolic time series provides better separation than MSE between EC and EO during resting states at each electrode. The fourth direction was to quantify the dynamics of physiological systems using Wavelet based entropy at multiple temporal scales. Wavelet entropy included Shannon, threshold, sure and norm using wavelet transform were computed. The results revealed that wavelet norm and sure entropies gave statistically significant results as compared to Shannon and threshold wavelet entropy at multiple temporal scales.