Self-Retrospect Periphery Gate Model and Its Applications - Cai, Xiuhua; Cao, Hongxing; Fang, Xiaoyi; Sun, Jingli; Cheng, Chen; Fan, Wenjie; Yu, Ying (Frontiers in Applied Mathematics and Statistics, 2022)
Not only relying on initial state, but also relying on states before, the principle of self-retrospect dynamic system has been developed to represent the changes of a system since1991. Afterwards the periphery theory was established, which studies the boundary of a system. We try to integrate the principle of self-retrospect system and periphery theory in this paper. Thus, self-retrospect periphery gate model, a new expression of temporal-spatial concept, has been derived to investigate the change of a system and forecast it in physics. Firstly, for the equation with time difference term that controls the motion of system, a difference-integral equation can be derived by introducing retrospect function and applying inner product, partial integral and mean value theorem. The principle of constructing and solving the difference-integral equation of system is referred to as the principle of self-retrospect dynamic systems, and the corresponding mathematical model is called the self-retrospect model. The principle of system self-retrospect has been applied to modeling, calculating and forecasting in many fields such as meteorology, oceanography, hydrology, market, agriculture, transportation, energy and so on. Secondly, the periphery is defined as an intermediary that can protect the system and exchange with the environment. It is a part of the system and adjacent to the environment. It has been applied in many fields since the periphery theory was put forward, such as physics, meteorology, water resources, economy as well as sports. Thirdly, the concept of periphery gate is embedded into the self-retrospect equation, and the self-retrospect gate model has been proposed, and the physical implication of the model is mentioned. Mathematical derivation of the model and its physical explanation are the main point of the paper. The applications of the model in physics and meteorology are discussed, as example, the relationship between heavy snowfall and airflow passage in Beijing was studied by means of synoptic meteorology in detail.