Shock propagation in cascade systems

In this paper, we study shock propagation in cascade systems which can be a model of outage of power systems and a model to spread a new fashion. Although stabilities of the cascade systems have been studied in scientific area, we give a new problem in view of control theory and develop system analysis of the model. Concretely, a new stability analysis of the cascade model is conducted, and we develop an invariant set theory of the cascade model which is an essential part of an algorithm to find initial subsystems that cause a global cascade in shock propagation.