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. 

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.