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)
By not only relying on the initial state but also relying on states before, the principle of a self-retrospect dynamic system has been developed to represent the changes in a system since 1991. Afterward, the periphery theory was established, which studies the boundary of a system. We try to integrate the principle of the self-retrospect system and periphery theory in this study. Thus, a 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 a time difference term that controls the motion of the system, a difference-integral equation can be derived by introducing a retrospect function and applying the inner product, partial integral, and mean value theorem. The principle of constructing and solving the difference-integral equation of the 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 is 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, the self-retrospect gate model has been proposed, and the physical implication of the model is mentioned. The mathematical derivation of the model and its physical explanation are the main points of the study. The applications of the model in physics and meteorology are discussed, for example, the relationship between heavy snowfall and airflow passage in Beijing was studied using synoptic meteorology in detail.