Dynamics and bifurcation in networks : theory and applications of coupled differential equations
- Philadelphia : Society for Industrial and Applied Mathematics, 2023
- xxxi, 834 p. ; ill., 27 cm
- Other titles in applied mathematics ; 185 .
Includes bibliographical references and index.
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.
9781611977325
Differential equations Qualitative theory Dynamical systems and ergodic theory Approximation methods Numerical treatment of dynamical systems Methods of simulation Theory of mathematical modeling