Golubitsky, Martin
Dynamic and bifurcation in networks : theory and applications of coupled differential equations - Philadelphia : Society for Industrial and Applied Mathematics, [2023] - 834 p.
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
9781611977325
Differential equations
Differential equations--Qualitative theory
Bifurcation theory
QA372 .G615
Dynamic and bifurcation in networks : theory and applications of coupled differential equations - Philadelphia : Society for Industrial and Applied Mathematics, [2023] - 834 p.
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
9781611977325
Differential equations
Differential equations--Qualitative theory
Bifurcation theory
QA372 .G615