基于Logistic模型的均值突变时间序列临界预警研究

对物理学中的非线性方程——Logistic方程解的稳定性进行分析, 发现当初值和参数取值一定时, 解具有从一种稳定状态突变到另一种稳定状态的特性. 突变的程度和速度与方程的控制参数有关, 可以用定义的突变强度指数来进行描述. 利用方程解的这一特性, 构造满足动力学结构突变的理想时间序列, 模拟气候系统中的均值突变, 考察物理量回复速率和回复力在系统趋近临界阈值时的临界行为, 研究其对系统突变的早期预警能力. 本文还讨论了当系统受到噪声信号干扰时, 回复速率和回复力仍然对系统突变有较好的预警. 最后, 对太平洋年代际振荡(PDO)指数序列进行检测, 检测结果表明早期预警信号出现在1973年前后, 而公认的PDO指数序列的突变发生在1976/1977年, 表明回复速率和回复力在一定程度上可以作为均值突变的早期预警信号.

The critical warning research of the mean time series mutations based on Logistic model

In this paper, we analyze the stability of solution of the nonlinear function of physics, the Logistic function. It is found that the solution has a special character that it can change abruptly from one stable state to another when the initial value and parameters of function are selected. Abrupt change level and abrupt change rate are related to parameters of function, which can be described by defining the abrupt change intensity index. By using the character of solution, we build an ideal time series to imitate climate abrupt change in mean of climate system, investigate what behaviors the recovery rate and recovery force can have when the system approaches to a critical threshold, and to ascertain how it warns the abrupt change of the system early. Besides, we also find that even the system is disturbed by some noise signals, the recovery rate and recovery force also make an early response to the arrival of the abrupt change of system. Finally, the result of testing the Pacific Decadal Oscillation (PDO) index showes that the early warning of the abrupt change appeared in 1973, much more early than the abrupt change of PDO index happening in 1976/1977, which means that the recovery rate and recovery force can be used as the early warning signals of the abrupt change in mean.