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Chapter 1. Introduction.- Part 1. Theory.- Chapter 2. Phase and amplitude description of complex oscillatory patterns in reaction diffusion systems.- Chapter 3. Reduced phase models of oscillatory neural networks.- Chapter 4. Nonautonomous attractors.- Chapter 5. Normal hyperbolicity for non-autonomous oscillators and oscillator networks.- Chapter 6. Synchronisation and non-autonomicity.- Chapter 7. Non-asymptotic-time dynamics.- Chapter 8. Synchronization of coupled oscillators - phase transitions and entropy production.- Part 2. Model-Driven and Data-Driven approaches.- Chapter 9. On localised modes in bio-inspired hierarchically organised oscillatory chains.- Chapter 10. Useful transformations from non-autonomous to autonomous systems.- Chapter 11. Coupling functions in neuroscience.- Chapter 12. Phase reconstruction with iterated Hilbert transforms.- Part 3. Biological Oscillators.- Chapter 13. Oscillations in yeast glycolysis Lars Folke Olsen and Anita Lunding.- Chapter 14. Oscillations, rhythms and synchronized time bases: the key signatures of life.- Chapter 15. Glycolytic oscillations in cancer cells.- Chapter 16. Mechanism and consequence of vasomotion.- Chapter 17. Biological oscillations of vascular origin and their meaning: in vivo studies of arteriolar vasomotion.- Chapter 18. Phase coherence of ﬁnger skin blood ﬂow oscillations induced by controlled breathing in humans.- Chapter 19. Complexity-based analysis of microvascular blood ﬂow in human skin.- Chapter 20. Modulations of heart rate, ECG, and cardio-respiratory coupling observed in polysomnography.- Chapter 21. Brain morphological and functional networks: implications for neurodegeneration.- Part 4. Applications.- Chapter 22. Predicting epileptic seizures - an update.- Chapter 23. General an sthesia and oscillations in human physiology: the BRACCIA project.- Chapter 24. Processed EEG as a measure of brain activity during anaesthesia.- Chapter 25. Medical products inspired by biological oscillators: intermittent pneumatic compression and the microcirculation.- Chapter 26. Phase coherence between cardiovascular oscillations in malaria: the basis for a possible diagnostic test.- Part 5. Outlook.- Chapter 27. Outlook.