A method for the global analysis of non-linear systems is presented which provides a framework for the analysis of both continuous and discrete-time non-linear systems for the diverse range of model types. By extending a numerical approach to enable the analysis of non-linear parametrized non-linear systems a global perspective is achieved that is difficult to obtain using analytical methods alone. Simple examples are used to illustrate how the method characterizes the system stability at the same time as detecting typical qualitative bifurcation phenomena. A non-linear feedback system is analysed in order to show how the approach provides both qualitative and quantitative information over a defined region of the system parameter space. The method proves to be a powerful tool which can be used to probe the non-linear characteristics of a system.