Dynamic Models and Control of Biological Systems

ISBN-13: 9781441903587 / Angielski / Twarda / 2009 / 275 str.

Vadrevu Sree Hari Rao; Ponnada Raja Sekhara Rao

Opis

Mathematical Biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biological sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems which arise in the biological sciences and gives some indication of the wide spectrum of questions that modeling can address.

Recenzje

From the reviews:

"The main aim of 'this monograph is to present an essentially self-contained account of the theory of mathematical model building of microbial populations', and the authors succeeded in accomplishing this from every angle. ... Another interesting aspect of this book is the section titled 'Notes and Remarks' at the end of each chapter to provide the reader additional material for further study and investigation. ... the book is a welcome addition to this growing and interesting field of convergence of life sciences, mathematics and engineering." (D. Subbaram Naidu, Amazon.com, December, 2013)

"The book is well organized and carefully written. ... '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', detailed step-by-step explanations of the main techniques are given, along with a selection of appropriate examples. ... The book should be of interest to graduate students and researchers working on differential equations and their applications; it can also be used for teaching advanced undergraduate and graduate courses." (Yuri V. Rogovchenko, Mathematical Reviews, Issue 2012 a)

Spis treści

Basic Models.- Chemostat Versus the Lake.- Instability Tendencies.- Self-Regulation.- Wall Growth.- Zones of No Activation.- Influence of the Control Mechanisms.- Parameter Estimation Using Dynamic Optimization.

Blurb

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 have become very popular since mathematical predictions can be tested in the laboratory employing a device known as the chemostat. Such models are called chemostat models. This book attempts to present a self contained account of mathematical model building theory of microbial populations.

Key Features:

Covers all fundamental concepts and mathematical skills needed to build models for microbial populations.

Provides an accessible and informative over view of known literature including several practical techniques.

Presents a comprehensive analysis of chemostat models and their limitations in adapting to natural lakes.

A thorough discussion on the design of biologically viable control mechanisms (termed bio-control mechanisms) to contain the instability tendencies.

Construction of a variety of Lyapunov functionals for global stability analysis.

This book is ideal for a general scientific and engineering audience requiring an in-depth exposure to current ideas, methods and models. The topics discussed can serve as a one to two semester course material for senior under graduate and graduate students. It is a useful reference for practitioners, researchers, and professionals in applied mathematics, biology, agriculture, limnology, chemical and civil engineering.