Phase Resetting in Medicine and Biology: Stochastic Modelling and Data Analysis

Synchronization processes are of great interest and importance in biology, medicine and physics. In particular, for the comprehension of brain function­ ing it appears inevitable that one should analyze neuronal synchronization processes. This book presents a new understanding of how a stimulus in­ fluences synchronization patterns of a population of oscillators. On the one hand, a variety of stimulation-induced dynamical phenomena will be pre­ sented; on the other hand, new data analysis tools will be developed which will serve as a link between theory and experiment. In this way it will be possible to use the theory presented here as a basis for the design and evalu­ and ation of stimulation experiments and stimulation techniques in medicine biology. We shall focus particularly on applications concerning the analysis of magnetoencephalography (MEG) and electroencephalography (EEG) data as well as deep brain stimulation techniques used in Parkinsonian patients. This book addresses graduate students, professors and scientists in vari­ ous fields including biology, mathematics, medicine, neuroscience, physiology and physics. Besides mathematically involved parts, the book also provides the reader with numerous illustrations and explications of the deep dynamical principles governing stimulation-induced desynchronization and synchroniza­ tion processes. Therefore this book will be of interest to a general readership, and those who are not familiar with mathematics should not be deterred by the formulas.