SYNCHRONIZATION IN DYNAMICAL NETWORKS: SYNCHRONIZABILITY, NEURAL NETWORK MODELS AND EEG ANALYSIS

Complex dynamical networks are ubiquitous in many fields of science from engineering to biology, physics, and sociology. Collective behavior, and in particular synchronization, is one of the most interesting consequences of interaction of dynamical systems over complex networks. Analyzing statistical and dynamical properties of complex networks may lead us to understand them deeper. This book discuses the problem of synchronizability in dynamical networks and gives some possible interpretations of that. Various methods for enhancing the synchronizability of dynamical networks through link weighting or rewiring is addressed. The book also studies the synchronization phenomenon in networks of model neurons and gives a simple model for investigating the behavior of interacting locally synchronized gamma oscillations. In the last section of the book the interdependencies within the time series obtained through electroencephalography is studied. Proper synchronization measures are introduced electroencephalography-specific maps for patients suffering from schizophrenia or Alzheimer?s disease are obtained.