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.

The effects of stochastic forcing on air-sea interaction, energy baiance ciimate modei is considered.The noniinear source is dynamicai heat transport.The roie to coupiing different temporai and spatiai scaies of the atmosphere is examined.A stochastic dynamicai modei of air-sea interaction is derived via the Fokker-Pianck eguation (FPE).The FPE from statisticai mechanics is used to obtain a time evoiution of the probabiiity density function and the ciimatic potentiai function.The matrix-continued fraction method (MCFM) is appiied to get the soiution with which effect of greenhouse gases was caicuiated.As a resuit, sea surface temperature rises by 1.2 K,meanwhiie the basic period is about 3~4 years and becomes ionger on doubiing CO₂.