A systematic approach is presented for predicting all the possible phase-plane diagrams of a system of two ordinary differential equations with widely separated time scales, and of the sequence of phase plane diagrams obtained by varying a parameter, i.e. bifurcation diagrams. The use of widely separated time scales enables the derivation of analytical algebraic expressions predicting all the transitions (bifurcations). A method is presented for a systematic finding of all the bifurcation diagrams for a system of two differential equations containing two parameters. The method is extended to systems containing many parameters. Application to the design and analysis and experimental observations are discussed.