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خالد بن ابراهيم بن عبدالله الحميزي

Professor

عميد عمادة البحث العلمي

كلية الهندسة
المبنى 3 - الدور الثاني ب29 كلية الهندسة - حاليا عمادة البحث العلمي مبنى 19 الدور الثاني
publication
Book
1996

Surveying a dynamical system: a study of the Gray-Scott reaction in a two-phase reactor

, Khalid Alhumaizi & Rutherford Aris . 1996

Series: Chapman & Hall/CRC Research Notes in Mathematics Series (Book 341)

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.

Publisher Name
CRC Press, Taylor & Francis Group
Publishing City
USA
more of publication
publications

Features

by Abdelhamid Ajbar & Khalid Alhumaizi
2011
Published in:
CRC Press, Taylor & Francis Group
publications

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…

by Khalid Alhumaizi & Rutherford Aris ,
1996
Published in:
CRC Press, Taylor & Francis Group