Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes properties such as mean, variance, trend, these shifts can manifest signal predictability, regularity, complexity, higher-order stochastic multi-sta...

Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of equations motion for nonlinear system from observed time series has been hot topic long time. Nevertheless, in practice only partial information available many systems which are very likely contaminated with noise. Here, based on the invariance evolution equat...