Details

Subject(s)

• Differential equations [Browse]
• Differential equations—Qualitative theory [Browse]
• Bifurcation theory [Browse]

Author

• Stewart, Ian, 1945- [Browse]

Publisher

• Society for Industrial and Applied Mathematics [Browse]

Series

Other titles in applied mathematics. [More in this series]

Restrictions note

Restricted to subscribers or individual electronic text purchasers.

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.

Show 31 more Contents items

Other format(s)

Also available in print version.

ISBN

1-61197-733-9

Publisher no.

OT185

LCCN

2022031029

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