000			02907 a2200241 4500
003			OSt
005			20240429124024.0
008			240429b |||||||| |||| 00| 0 eng d
020			_a9781611977325
040			_aICTS-TIFR
050			_aQA372 .G615
100			_aGolubitsky, Martin
245			_aDynamic and bifurcation in networks _b: theory and applications of coupled differential equations
260			_bSociety for Industrial and Applied Mathematics, _aPhiladelphia : _c[2023]
300			_a834 p.
505			_aChapter 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
520			_aThis 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
650			_aDifferential equations
650			_aDifferential equations--Qualitative theory
650			_aBifurcation theory
700			_aStewart, Ian
942			_2lcc _cBK
999			_c35088 _d35088