Dynamics and bifurcation in networks : theory and applications of coupled differential equations / Martin Golubitsky, The Ohio State University, Ian Stewart, University of Warwick.
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Summary note
In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book's main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of "admissible" ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems; develop connections between network architecture and the typical dynamics and bifurcations of these equations; and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions.
Bibliographic references
Includes bibliographical references (pages 773-812) and index.
System details
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Source of description
Description based on title page of print version.
Contents
Why networks?
Examples of network models
Network constraints on bifurcations
Inhomogeneous networks
Homeostasis
Local bifurcations for inhomogeneous networks
Informal overview
Synchrony, phase relations, balance, and quotient networks
Formal theory of networks
Formal theory of balance and quotients
Adjacency matrices
ODE-equivalence
Lattices of colorings
Rigid equilibrium theorem
Rigid periodic states
Symmetric networks
Spatial and spatiotemporal patterns
Synchrony-breaking steady-state bifurcations
Nonlinear structural degeneracy
Synchrony-breaking Hopf bifurcation
Hopf bifurcation in network chains
Graph fibrations and quiver representations
Binocular rivalry and visual illusions
Decision making
Signal propagation in feedforward lifts
Lattices, rings, and group networks
Balanced colorings of lattices
Symmetries of lattices and their quotients
Heteroclinic cycles, chaos, and chimeras
Epilogue
Appendix A. Liapunov-Schmidt reduction
Appendix B. Center manifold reduction
Appendix C. Perron-Frobenius theorem
Appendix D. Differential equations on infinite networks.
Other format(s)
Also available in print version.
ISBN
1-61197-733-9
Publisher no.
OT185
LCCN
2022031029
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