多尺度正负反馈交替论模型及其应用

The model of multi-scale alternate positive negative feedbackics and its applications

结合物质系统由量变到质变而呈现"平稳→剧变→再平稳→再剧变"这一变化规律,基于正负反馈交替论思想,提出了多尺度正负反馈交替论的数学模型.该模型引入等效正、负反馈作用,以状态变化速度作为第一尺度、状态变化加速度作为第二尺度进行等效正、负反馈作用的判定,根据状态变化剧烈程度以及剧烈变化趋势,将状态稳定性分离,以动力学方程形式表述物质系统的上述变化规律.该模型建立方法简单、实施方便,无需系统的内在机理或先验知识,是一种基于观测数据的通用模型.将该模型应用于时间序列预测,分别以空气质量指数AQI和大气主要污染物PM2.5数据为基础,进行系统建模及预报的仿真研究.结果表明,该模型能较准确反映系统的变化规律,能有效进行预报,且精度高,为具有量变引起质变而呈现出这一变化规律的复杂系统建模及预测提供了一种新颖而有效的手段.

Combining with the material systems whose state changes from stabilization to revulsion and then restabilization to re-revulsion due to quantitative and qualitative changes, the mathematical model of multi-scale alternate positive negative feedbackics is proposed based on ideas of the alternate positive negative feedbackics. The equivalent positive and negative feedbacks are introduced into the model and are discriminated by the state change speed as the first scale and its acceleration as the second scale. The states stability are divided according to the change intensity of the state and the trend of changes, and the above mentioned variation is expressed in the form of dynamic equations. The model establishing method is simple and easy to implement, and it is a general model based on observation data without needing the internal mechanism of the system or priori knowledge. The model is applied in time series forecast, and based on the air quality index of AQI data and the index of PM2.5 which is the main atmospheric pollutants, the model is established and used to forecast respectively. The results show that the model can reflect the variation of the system accurately and be effectively applied to forecast and has high precision. The model provides a novel and effective means for modeling and forecasting of the complex system whose state changes conform to the above law.