The threshold values that can enter the system into a chaos state as well as a great periodic state can be calculated, while is established. When the value of is fi xed, the system will change regularly with the change of .Now,let 1and 0.5, the parameter is gradually increased from zero. Using (18), for 0.3765, the system will appear in the chaotic state. For the typical system of (2), the threshold value for en- tering into the great periodic motion is numerically determined 0.8275). The can be set to a value a little smaller than the critical value . So the system is put into the critical state (chaos, but on the verge of changing to the great periodic mo- tion). The system state changes from the periodic state to chaos state are very slow; while the system changes into the great pe- riodic from the chaos state are very fast. So the latter domain is selected for the detection of islanding phenomenon.