Abstract: The approximate analysis of differential systems by applying the theory of regional analysis, is described. It supplies a formularization and calculating programme for algebraic limit cycle of second degree in a type of differential systems of third degree, and also for critical value of damping resistance in power systems. This new method simplifies the traditional method, hence it is acceptable and applicable for engineers. Finally, a few of examples are given based on this method.

Key words: regional analysis, limit cycle, critical value of damping resistance, removing the overvoltage of dividing frequency resonance