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

Abstract

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.