Abstract: The paper involves thorough study of non-linear vibratory oscillators and numerical methodology to analyse and resolute the non-linear dynamical world. The study involves the analysis of non-linear oscillators like the Van der Pol Oscillator and Duffing Oscillator. Application of regular perturbation method in the oscillator is also demonstrated. The equilibrium and stability analysis of the oscillators with graphical representation is simulated through XPP-AUT and MATLAB.