Abstract:On the basis of the theory for dissipative structure, the main characteristics of Rundle model earthquake are studied in detail.It is found that the double-stable states and the cusp catastrophe are shown in the process of fault dislocation for Rundle model.There are the hysteresis loop of fault dislocation, as the external stress changes between the critical values pc and -pc, and catastrophes occurred at the critical values pc and -pc.The former corresponds to the accumulation of strain energy of the system, and the latter (i.e., strong earthquakes)is the main mechanism for energy dissipation of the system.