document: Despite the ubiquity of time-dependent dynamical systems in nature, there has been relatively little work done on the analysis of time series from such systems. Mathematically they are known as non-autonomous systems, which are named as such because, unlike autonomous systems, in addition to the points in space over which they are observed they are also influenced by the points in time. Recently there has been much work on the direct ‘bottom-up’ approach to these systems, which includes the introduction of a subclass known as chronotaxic systems that are able to model the stable but time-varying frequencies of oscillations in living systems [8,9]. In contrast, the time series analysis of these systems, referred to as the inverse or ‘top-down’ approach, has not been studied in detail before. This is partly because non-autonomous systems can still be analysed in the same way as other types of systems in both the deterministic [10] and the stochastic [11] regime. However, it is now argued that this type of analysis is insufficient and that an entirely new analytical framework is required to provide a more useful picture of such systems. In the case of chronotaxic systems some methods have already been developed for the inverse approach and they have shown to be useful in analysing heart rate variability [12]. A general and dedicated procedure for analysing non-autonomous systems has still not been tackled though.
extractive_keyphrases: analysis of time series analytical framework autonomous systems chronotaxic systems deterministic heart rate variability inverse living systems stochastic time series analysis
abstractive_keyphrases: ‘bottom-up’ approach inverse approach model the stable but time-varying frequencies non-autonomous systems time-dependent dynamical systems ‘top-down’