Dynamic and bifurcation in networks : theory and applications of coupled differential equations

By: Golubitsky, MartinContributor(s): Stewart, IanPublication details: Philadelphia : Society for Industrial and Applied Mathematics, [2023]Description: 834 pISBN: 9781611977325Subject(s): Differential equations | Differential equations--Qualitative theory | Bifurcation theoryLOC classification: QA372 .G615
Contents:
Chapter 1: Why Networks? Chapter 2: Examples of Network Models Chapter 3: Network Constraints on Bifurcations Chapter 4: Inhomogeneous Networks Chapter 5: Homeostasis Chapter 6: Local Bifurcations for Inhomogeneous Networks Chapter 7: Informal Overview Chapter 8: Synchrony, Phase Relations, Balance, and Quotient Networks Chapter 9: Formal Theory of Networks Chapter 10: Formal Theory of Balance and Quotients Chapter 11: Adjacency Matrices Chapter 12: ODE-Equivalence Chapter 13: Lattices of Colorings Chapter 14: Rigid Equilibrium Theorem Chapter 15: Rigid Periodic States Chapter 16: Symmetric Networks Chapter 17: Spatial and Spatiotemporal Patterns Chapter 18: Synchrony-Breaking Steady-State Bifurcations Chapter 19: Nonlinear Structural Degeneracy Chapter 20: Synchrony-Breaking Hopf Bifurcation Chapter 21: Hopf Bifurcation in Network Chains Chapter 22: Graph Fibrations and Quiver Representations Chapter 23: Binocular Rivalry and Visual Illusions Chapter 24: Decision Making Chapter 25: Signal Propagation in Feedforward Lifts Chapter 26: Lattices, Rings, and Group Networks Chapter 27: Balanced Colorings of Lattices Chapter 28: Symmetries of Lattices and Their Quotients Chapter 29: Heteroclinic Cycles, Chaos, and Chimeras Chapter 30: Epilogue Appendix A: Liapunov-Schmidt Reduction Appendix B: Center Manifold Reduction Appendix C: Perron-Frobenius Theorem Appendix D: Differential Equations on Infinite Networks
Summary: This 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.---- summary provided by the publisher
List(s) this item appears in: New Arrivals of books | New Arrivals
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
Item type Current library Collection Shelving location Call number Status Date due Barcode Item holds
Book Book ICTS
Mathematics Rack No 6 QA372 .G615 (Browse shelf (Opens below)) Checked out 08/02/2024 02814
Total holds: 0

Chapter 1: Why Networks?
Chapter 2: Examples of Network Models
Chapter 3: Network Constraints on Bifurcations
Chapter 4: Inhomogeneous Networks
Chapter 5: Homeostasis
Chapter 6: Local Bifurcations for Inhomogeneous Networks
Chapter 7: Informal Overview
Chapter 8: Synchrony, Phase Relations, Balance, and Quotient Networks
Chapter 9: Formal Theory of Networks
Chapter 10: Formal Theory of Balance and Quotients
Chapter 11: Adjacency Matrices
Chapter 12: ODE-Equivalence
Chapter 13: Lattices of Colorings
Chapter 14: Rigid Equilibrium Theorem
Chapter 15: Rigid Periodic States
Chapter 16: Symmetric Networks
Chapter 17: Spatial and Spatiotemporal Patterns
Chapter 18: Synchrony-Breaking Steady-State Bifurcations
Chapter 19: Nonlinear Structural Degeneracy
Chapter 20: Synchrony-Breaking Hopf Bifurcation
Chapter 21: Hopf Bifurcation in Network Chains
Chapter 22: Graph Fibrations and Quiver Representations
Chapter 23: Binocular Rivalry and Visual Illusions
Chapter 24: Decision Making
Chapter 25: Signal Propagation in Feedforward Lifts
Chapter 26: Lattices, Rings, and Group Networks
Chapter 27: Balanced Colorings of Lattices
Chapter 28: Symmetries of Lattices and Their Quotients
Chapter 29: Heteroclinic Cycles, Chaos, and Chimeras
Chapter 30: Epilogue
Appendix A: Liapunov-Schmidt Reduction
Appendix B: Center Manifold Reduction
Appendix C: Perron-Frobenius Theorem
Appendix D: Differential Equations on Infinite Networks

This 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.---- summary provided by the publisher

There are no comments on this title.

to post a comment.