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Tackling the Inverse Problem for Non-Autonomous Systems

Part of the Springer Theses Book Series

DOI: 10.1007/978-3-319-00753-3

ISBN: 978-3-319-00752-6

Publisher: Springer International Publishing - Springer Journals

Aug 28, 2013

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Chapter 1Introduction

Stankovski, Tomislav

Pages: 1 –8

[The common assumption that a dynamical system found in nature can be considered as isolated and autonomous is frequently a poor approximation. In reality, there are always external influences, and these are often too strong to ignore. In the case of interacting oscillatory systems, they may e.g....
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Chapter 2Theoretical Background: Non-Autonomous Systems and Synchronization

Stankovski, Tomislav

Pages: 9 –35

[The theoretical framework for the analysis of synchronization between non-autonomous oscillating systems is discussed. Multiple-scale analysis is applied to a phase oscillator model with slowly varying frequency. This analysis reveals the analytic form of the synchronization state with respect...
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Chapter 3Bayesian Inference of Time-Evolving Coupled Systems in the Presence of Noise

Stankovski, Tomislav

Pages: 37 –74

[A method is introduced for the analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be...
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Chapter 4Application to Life Sciences

Stankovski, Tomislav

Pages: 75 –108

[The proposed theory and methods are applied for the analysis of biological oscillatory systems affected by external dynamical influences. The main investigation is performed on physiological measurements under conditions where the breathing frequency is varied linearly, thus introducing a...
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Chapter 5Analogue Simulation and Synchronization Analysis of Non-Autonomous Oscillators

Stankovski, Tomislav

Pages: 109 –117

[The study focuses on the analysis of an analogue simulation of two nonautonomous van der Pol oscillators. The oscillators are unidirectionally coupled, and the frequency of the first oscillator is externally and periodically perturbed. The analogue simulation presents another circumstance where...
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Chapter 6Conclusion

Stankovski, Tomislav

Pages: 119 –122

[This work studies the effect of external dynamical sources on interacting self-sustained oscillators.]

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