Abrupt Change Detection Method Based on Features of Lorenz Trajectories

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.