Disorder in Complex Networks

This book presents a comprehensive mathematical approach to study the role of disorder in complex network systems. While most studies of complex networks assume nodes to be homogeneous and the connections to be perfectly symmetric, these assumptions do not hold in real-world applications. In recent years, this realization has led to a growing interest in developing methods to study the interplay between disorder in networks and their collective response. The book describes how to use current ideas and methods from dynamical systems with symmetry, i.e. equivariant bifurcation theory, to model, analyze, and predict the behavior of complex networks where disorder can appear, naturally, through variations in parameter values or imperfections of individual nodes, and through broken connections that lead to asymmetries in a network. A common set of methods that can be adapted to study a wide range of systems where disorder might appear are introduced and can be applied to robotics, precision timing devices, networks of nano oscillators for microwave frequency generation, sensors, gyroscopes, and multi-frequency converters. The author also discusses a fascinating question: whether disorder can influence the collective output of a network. As a result, this book uniquely presents systematic methods to determine how this apparent paradox can lead to the emergence of stable patterns of behavior of a network.