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This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described.
Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas.
List of contents
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 ow oscillations induced by controlled breathing in humans.- Chapter 19. Complexity-based analysis of microvascular blood ow 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 anæsthesia 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.
