Abstract: The system boundary which plays a role in:Ι defending the existence of the system; and Ⅱ exchanging between the system and its environment is defined as a shell (Jieke).Some basic concepts in Jieke theory are described.Some applications of the theory are presented too, in particular,considering switch function of the gate in system, a new discrete logistical model is established.Mapping calculation for the model was conducted.Then nonlinear features of the model with parameter variation were analyzed and irrational numbers and cyclic small numbers are obtained.

Key words: system science, jieke, logistic model, life growth