It has been recognized that the evaporation process is one of the pivotal mechanisms driving thermo-acoustic instability in gas turbines and rockets in particular. In this regard, this study is principally focused on studying the evaporation process relevant to thermo-acoustic instability from three complementary viewpoints in an effort to contribute to an overall instability model driven primarily by evaporation in gas turbine combustors. Firstly, a state of the art LES algorithm is employed to validate an evaporation model to be employed in predictive modelling regarding combustion instabilities. Good agreement between the numerical predictions and experimental data is achieved. Additionally, transient sub-critical droplet evaporation is investigated numerically. In particular, a numerical method is proposed to capture the extremely important pressure-velocity-density coupling. Furthermore, the dynamic system nonlinear behaviour encountered in classical thermo-acoustic instability is investigated. The Poincaré map is adopted to analyse the stability of a simple non-autonomous system considering a harmonic oscillation behaviour for the combustion environment. The bifurcation diagram of a one-mode model is obtained where the analysis reveals a variety of chaotic behaviours for some select ranges of the bifurcation parameter. The bifurcation parameter and the corresponding period of a two-mode dynamic model are calculated using both analytical and numerical methods. The results computed by different methods are in good agreement. In addition, the dependence of the bifurcation parameter and the period on all the relevant coefficients in the model is investigated in depth. Moreover, a discrete dynamic model accounting for both combustion and vaporization processes is developed. In terms of different bifurcation parameters relevant to either combustion or evaporation, various bifurcation diagrams are presented. As part of the nonlinear characterization, the governing process Lyapunov exponent is calculated and employed to analyze the stability of the particular dynamic system. The study has shown conclusively that the evaporation process has a significant impact on the intensity and nonlinear behaviour of the system of interest, vis-à-vis a model accounting for only the gaseous combustion process. Furthermore, two particular nonlinear control methodologies are adopted to control the chaotic behaviour displayed by the particular aperiodic motions observed. These algorithms are intended to be implemented for control of combustion instability numerically and experimentally to provide a rational basis for some of the control methodologies employed in the literature. Finally, a state of the art neural network is employed to identify and predict the nonlinear behaviour inherent in combustion instability, and control the ensuing pressure oscillations. Essentially, the NARMAX model is implemented to capture nonlinear dynamics relating the input and output of the system of interest. The simulated results accord with the results reported. Moreover, a control system using the NARMA-L2 algorithm is developed. The simulation conclusively points to the fact that the amplitude of pressure oscillations can be attenuated to an acceptable level and the controller proposed may be implemented in a practical manner.