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

Publication details: Philadelphia : Society for Industrial and Applied Mathematics, [2023]Description: 834 pISBN: 9781611977325Subject(s): Differential equations | Differential equations--Qualitative theory | Bifurcation theoryLOC classification: QA372 .G615Item type | Current library | Collection | Shelving location | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|---|

Book | ICTS | Mathematics | Rack No 6 | QA372 .G615 (Browse shelf (Opens below)) | Available | 02814 |

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

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