Significant changes in a system's dynamics can be understood through modifications in the topological structure of its flow in phase space. In the Earth's climate system, such changes are often referred to as tipping points. One of the large-scale components that may pass a tipping point is the Atlantic Meridional Overturning Circulation. Our understanding of tipping points can be enhanced using a recently proposed mathematical concept-the templex-which enables the identification of dynamics of different classes. Unlike traditional topological invariants, templex properties describe not only the topology of the underlying structure of a set of points in phase space associated with a finite time series but also the non-equivalent pathways allowed by the flow around that structure. In this study, we investigate the dynamics produced by an idealized autonomous model and its nonautonomous counterpart to consider long-term climate changes and reproduce phenomena occurring during different epochs, such as glacial and interglacial intervals. In the nonautonomous system, the trajectory visits two distinct domains in phase space, one of which shares certain properties with those found in the autonomous case. A dissection of the templex and the definition of active templex properties improve our understanding of how the system tips from one regime to another. We also discuss the relationship between our results and the nonautonomous model's pullback attractor.
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