Time-dependent dynamics is ubiquitous in the natural world and beyond. Effectively analysing its presence in data is essential to our ability to understand the systems from which it is recorded. ...However, the traditional framework for dynamics analysis is in terms of time-independent dynamical systems and long-term statistics, as opposed to the explicit tracking over time of time-localised dynamical behaviour. We review commonly used analysis techniques based on this traditional statistical framework—such as the autocorrelation function, power-spectral density, and multiscale sample entropy—and contrast to an alternative framework in terms of finite-time dynamics of networks of time-dependent cyclic processes. In time-independent systems, the net effect of a large number of individually intractable contributions may be considered as noise; we show that time-dependent oscillator systems with only a small number of contributions may appear noise-like when analysed according to the traditional framework using power-spectral density estimation. However, methods characteristic of the time-dependent finite-time-dynamics framework, such as the wavelet transform and wavelet bispectrum, are able to identify the determinism and provide crucial information about the analysed system. Finally, we compare these two frameworks for three sets of experimental data. We demonstrate that while techniques based on the traditional framework are unable to reliably detect and understand underlying time-dependent dynamics, the alternative framework identifies deterministic oscillations and interactions.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Oscillatory dynamics pervades the universe, appearing in systems of all scales. Whilst autonomous oscillatory dynamics has been extensively studied and is well understood, the very important problem ...of non-autonomous oscillatory dynamics is less well understood. Here, we provide a framework for non-autonomous oscillatory dynamics, within which we can define intermittent phenomena such as intermittent phase synchronisation. Moreover, we demonstrate this framework with a coupled pair of non-autonomous phase oscillators as well as a higher-dimensional system comprising of two interacting phase-oscillator networks.
•A new framework for phase-dynamics phenomena in non-autonomous oscillatory systems.•Interactions between pairs of non-autonomous oscillators and networks are considered.•Intermittent synchronisation is formulated mathematically.•Relevant for many real-world problems.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Living systems are defined by their thermodynamic openness, by the fact that energy and matter are able to cross their boundaries. Without this capability to interact with their environment, living ...systems would be unable to support their life-sustaining functions. As a result of this continual interaction with its environment, the interior processes of a living system is forced to operate far from any equilibrium. Indeed, any system that is in equilibrium internally or with its environment could reasonably be characterised as a dead one.The dynamics of systems that are operating far from equilibrium, however, are far from understood. In this thesis, we build on an existing framework for understanding these dynamics, based in the finite-time analysis of non-autonomous oscillatory processes. This approach is motivated by a key consequence of thermodynamic openness — to introduce time-dependence to the open system. We develop an original mathematical model for the energy metabolism of cells using inter-coupled networks of non-autonomous phase oscillators, with intra-network weighted coupling. The effect of each of this model’s components on its dynamics and stability is numerically analysed. Experimental data of the metabolism of HeLa cells is analysed, finding the fundamental frequencies of this process. This analysis is used to demonstrate the capability of the model to reproduce the complex dynamics of the experiment, and this is contrasted to a comparable model of an alternative framework.It is this capacity of non-autonomous oscillations to simply and deterministically produce apparently highly complex dynamics that justifies our application of them to this problem. We demonstrate it further by viewing them through the framework of statistical time-series analysis, finding that even a single non-autonomous oscillator can appear to be 1/fβnoise in a power-spectral density estimation. Autonomous systems are shown to only present as noise when there are many of them, and hence it is the introduction of time-dependence that generates such complexity so readily. We demonstrate that this also occurs for coupled networks of non-autonomous oscillators, and in real experimental data. Analysis tools based in a finite-time framework, however, are shown to detect informative deterministic frequencies and couplings in both the numerical and experimental cases.Overall, this thesis demonstrates that networks of non-autonomous oscillations are physically linked to living systems through the time-dependence introduced by thermodynamic openness. Additionally, it is shown that they are able to reproduce living systems’ complex dynamics in a simple and usable way. Finally, it is established that much greater information about such an open system can be gained when they are analysed with this time-dependent deterministic framework in mind.
