Abstract
This paper presents a definition of bifurcation-type abrupt changes based on the bifurcation features of Lorenz trajectories. These abrupt changes are the result of the transition behavior of dynamical system trajectories among different equilibrium regions. We demonstrate that these bifurcation-type jumps can better reflect the nature of abrupt change. In analyzing the features of Lorenz equation trajectories, a dynamical method for detecting bifurcation-type abrupt changes is presented. A numerical solution of the Lorenz equation is adopted, using a curve integral or vector product to construct a time series of positive and negative values. Changes in the sign of this time series accurately determine whether the trajectory is in the right or left equilibrium region, and the points at which the time series is equal to zero are the times at which the trajectory jumps between different equilibrium regions, that is, the occurrence times of bifurcation-type abrupt changes. This method is completely dependent on the dynamical characteristics of the system. A theoretical approach for detecting abrupt climate changes based on the dynamical characteristics of the atmospheric model is described. Compared with the original method of identifying abrupt climate changes, this method has dynamic significance and can detect abrupt changes in multi-dimensional time series. Although this method can be applied theoretically, applications to real atmospheric data first require the data to be smoothed.
Highlights
Abrupt changes are common phenomena in nature, and in human and social activities
The rotation direction of the pink and green transition trajectories is bound to change. In view of these characteristics of the bifurcation-type abrupt change, we propose a method for their detection that is helpful in classifying and detecting abrupt changes in the atmosphere
Based on the trajectories of the Lorenz equation, jumps among different equilibrium points have been defined as bifurcation-type abrupt changes
Summary
Abrupt changes are common phenomena in nature, and in human and social activities. Such phenomena have been studied in atmospheric science [1], oceanography [2], geology [3], geography [4], botany [5], zoology [6], medical science [7], economics [8], and sociology [9]. Catastrophe theory has been applied in various disciplines, such as gene mutations in biology [5,6], the adjustment of industrial structures in the field of economics [8], and the study of abrupt climate change in atmospheric science [14]. In all of these fields, catastrophe theory has been used to predict the changing behavior of complex and disordered systems. Whereas statistical algorithms have been used to study abrupt changes in previous papers, we describe a method for abrupt change detection of the atmospheric system’s dynamic features. This paper presents a definition and detection method for abrupt climate changes from the perspective of ordinary differential equation trajectories
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