Scientific Computation

Computational Methods in Bifurcation Theory and Dissipative Structures

Authors: Kubicek, M., Marek, Milos

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"Dissipative structures" is a concept which has recently been used in physics to discuss the formation of structures organized in space and/or time at the expense of the energy flowing into the system from the outside. The space-time structural organization of biological systems starting from the subcellular level up to the level of ecological systems, coherent structures in laser and of elastic stability in mechanics, instability in hydro­ plasma physics, problems dynamics leading to the development of turbulence, behavior of electrical networks and chemical reactors form just a short list of problems treated in this framework. Mathematical models constructed to describe these systems are usually nonlinear, often formed by complicated systems of algebraic, ordinary differ­ ential, or partial differential equations and include a number of character­ istic parameters. In problems of theoretical interest as well as engineering practice, we are concerned with the dependence of solutions on parameters and particularly with the values of parameters where qualitatively new types of solutions, e.g., oscillatory solutions, new stationary states, and chaotic attractors, appear (bifurcate). Numerical techniques to determine both bifurcation points and the depen­ dence of steady-state and oscillatory solutions on parameters are developed and discussed in detail in this text. The text is intended to serve as a working manual not only for students and research workers who are interested in dissipative structures, but also for practicing engineers who deal with the problems of constructing models and solving complicated nonlinear systems.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-642-85957-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-642-85959-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Computational Methods in Bifurcation Theory and Dissipative Structures
Authors
Series Title
Scientific Computation
Copyright
1983
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-3-642-85957-1
DOI
10.1007/978-3-642-85957-1
Softcover ISBN
978-3-642-85959-5
Series ISSN
1434-8322
Edition Number
1
Number of Pages
XII, 243
Topics