Dynamics and bifurcation in networks : theory and applications of coupled differential equations In recent years there has been an explosion of interest in network based modeling in many branches of science including biology physics chemistry computer science electrical and electronic engineering psychology and sociology. This book attempts a synthesis of some of the common features of many such models providing a general framework analogous to the modern theory of nonlinear dynamical systems. Most chapters begin with a nontechnical introductory overview followed by a more detailed exposition. The main themes are how networks lead to behavior that would not be typical in a general dynamical system and how the architecture of the network influences this behavior. A formal definition of a network and the associated class of admissible ordinary differential equations is introduced in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. Connections between network architecture and the typical dynamics and bifurcations of these equations are introduced. Applications of this formalism to various areas of science including gene regulatory networks animal locomotion decision making homeostasis binocular rivalry and visual illusions are discussed