Surveying a Dynamical System: A Study of the Gray-Scott Reaction in a Two-Phase Reactor

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Khalid Alhumaizi (King Saud University) Rutherford Aris

Surveying a Dynamical System

A Study of the Gray-Scott Reaction in a Two-Phase Reactor

Khalid Alhumaizi (King Saud University), Rutherford Aris

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English

CRC Press
15 May 1996

Differential calculus & equations; Chaos theory; Maths for scientists; Maths for engineers

Series: Chapman & Hall/CRC Research Notes in Mathematics Series

When a dynamical system has a large number of parameters it is not possible to get a completely comprehensive picture of all the types of behavior that it may display and one must be content with surveying the system along various corridors of lower dimension. Using an example with three differential equations and six parameters it is shown how the available methods of singularity theory, bifurcation analysis, normal forms, etc. can be used to build up a picture of varied and interesting behavior. The model is a generalization of the Gray-Scott reaction scheme in a single stirred vessel to a two-phase reactor consisting of a reaction chamber and a reservoir communicating with each other through a semi-permeable membrane. Two forms exist according as to whether A is fed to the reactor and B to the reservoir or vice-versa, and show interesting differences of behavior. Both models undergo Hopf bifurcations, pitchfork transitions, have homoclinic orbits, take the period doubling route to chaos and one gets there by intermittency. Besides being of interest to mathematicians as an ecological study of a differentiable system, it is hoped that, though idealized, the fact that it corresponds closely to a real type of reactor will make it attractive to control engineers and others as a testing ground for their various methods and devices. This book will be of particular interest to students and researchers in mathematics and engineering , particularly those working in bifurcation or chaos theory.

By: Khalid Alhumaizi (King Saud University), Rutherford Aris
Imprint: CRC Press
Country of Publication: United Kingdom
Volume: 341
Dimensions: Height: 246mm, Width: 174mm, Spine: 18mm
Weight: 603g
ISBN: 9780582246881
ISBN 10: 0582246881
Series: Chapman & Hall/CRC Research Notes in Mathematics Series
Pages: 352
Publication Date: 15 May 1996
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Introduction, Mathematical modeling, Steady state analysis, Steady state analysis: Model I, Steady state analysis: Model II, Dynamics - theory, Dynamics - Model I, Dynamics - Model II, Chaos - theory, Chaos - Model I, Chaos - Model II, Summary and conclusions

Khalid Alhumaizi, Rutherford Aris

Reviews for Surveying a Dynamical System: A Study of the Gray-Scott Reaction in a Two-Phase Reactor

The authors of this book made the interesting and inspiring choice to approach this problem in a very applied fashiononly two related, relatively simple, three-dimensional ordinary differential equations are studiedThe nice thing about this book is that the two models studied here are not completely 'toy models' -Nonlinear Science Today, November 1996