Elsevier S & T

Handbook of Dynamical Systems

Fiedler, B.

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Table of contents
  • Cover
  • Contentsxi
  • Prefacev
  • List of Contributorsix
  • Part A: Finite-Dimensional Methods1
  • Chapter 1. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators3
  • Chapter 2. Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere55
  • Chapter 3. Geometric singular perturbation analysis of neuronal dynamics93
  • Part B: Numerics147
  • Chapter 4. Numerical continuation, and computation of normal forms149
  • Chapter 5. Set oriented numerical methods for dynamical systems221
  • Chapter 6. Numerics and exponential smallness265
  • Chapter 7. Shadowability of chaotic dynamical systems313
  • Chapter 8. Numerical analysis of dynamical systems345
  • Part C: Topological Methods391
  • Chapter 9. Conley index393
  • Chapter 10. Functional differential equations461
  • Part D: Partial Differential Equations501
  • Chapter 11. Navier-Stokes equations and dynamical systems503
  • Chapter 12. The nonlinear Schrödinger equation as both a PDE and a dynamical system599
  • Chapter 13. Pattern formation in gradient systems677
  • Chapter 14. Blow-up in nonlinear heat equations from the dynamical systems point of view723
  • Chapter 15. The Ginzburg-Landau equation in its role as a modulation equation759
  • Chapter 16. Parabolic equations: asymptotic behavior and dynamics on invariant manifolds835
  • Chapter 17. Global attractors in partial differential equations885
  • Chapter 18. Stability of travelling waves983
  • Author Index1057
  • Subject Index1077
Book details
  • Vendor Elsevier S & T
  • SKU 9780444501684
  • ISBN-13 9780080532844
  • Author Fiedler, B.
  • Category Mathematics
  • Subject Applied

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Description eBook delivery & access Reviews
This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from
interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers.



The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.



While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name
just a few, are ubiquitous dynamical concepts throughout the articles.