Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system

Abstract

This paper addresses the transient behavior mechanism analysis of a new chaotic system. Interesting transient behaviors of the new system are analyzed under the attractor merging crisis. The transient chaos and transient quasi-periodic behaviors are observed, under the boundary crisis, when the system has two stable equilibria. Furthermore, the reason of the two transient behaviors is revealed, with the conditions and relevant threshold for the boundary crisis are found, by introducing a simplified method of Lorenz time series. The lifetime of transient quasi-periodicity and parameters are found to meet the power-law distribution and have long memory, which indicates that the lifetime of transient quasi-periodicity is predictable. Therefore, the transient quasi-periodicity has potential values in the field of weak signal amplitude prediction.