Dynamic Models and Control of Biological Systems
Mathematical modeling in the biological sciences is growing exponentially because the general area provides exciting problems from biology to medicine, and this goes under the name mathematical biology. Moreover, models of the growth of microorganisms hav
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Vadrevu Sree Hari Rao Ponnada Raja Sekhara Rao
Dynamic Models and Control of Biological Systems
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Vadrevu Sree Hari Rao Department of Mathematics Jawaharlal Nehru Technological University Hyderabad, 500 085 (A.P.), INDIA [email protected]
Ponnada Raja Sekhara Rao Department of Technical Education A.P., Hyderabad Government Polytechnic for Women Gujjanagundla, Guntur-522 004 Andhra Pradesh, India [email protected]
ISBN 978-1-4419-0358-7 e-ISBN 978-1-4419-0359-4 DOI 10.1007/978-1-4419-0359-4 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009926036 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To the sacred memory of my beloved parents late Smt. Vadrevu Satyavathi late Sri Vadrevu Seshagiri Rao —————V. Sree Hari Rao
To nature for continued inspiration ————P. Raja Sekhara Rao
Preface
Our aim in this monograph is to present an essentially self-contained account of the theory of mathematical model building of microbial populations. The emphases and selection of topics reflect our own involvement in the field over the past 10 years and our intent has been to stress the ideas and methods of analysis besides describing the most general and far-reaching results possible. This monograph includes published work as well as work presented at various seminars and conferences. There has been much ferment in this field during the past 15 years resulting in numerous publications with various methods and theoretical arguments. Much experience has been gained from this research during the past decade by researchers that include mathematicians, biologists, limnologists, and chemical and civil engineers. Now it is time to crystallize these concepts into a simple ready-to-use format to enable the implementation of these models by practicing field scientists. Thus, the first and foremost aim of the authors is to encourage others to consider and apply the results and the tools discussed in this book. Also, it is an attempt by the authors, a mathematician with an enthusiasm for biology and a biologist with an interest in mathematics, to encourage and promote the quintessential aspects of a collaborative dialogue between their respective disciplines. Mathematical models that descr
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