Lectures on Nonlinear-differential-equation Models in Biology PDF Download

Author: James Dickson Murray
Publisher: Oxford University Press, USA
ISBN:
Category : Mathematics
Languages : en
Pages : 392

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Author: Stavros Busenberg
Publisher: Springer Science & Business Media
ISBN: 3642456928
Category : Mathematics
Languages : en
Pages : 276

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Book Description
The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.

Author: Ansgar Jüngel
Publisher: Springer Science & Business Media
ISBN: 3709106095
Category : Mathematics
Languages : en
Pages : 195

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The papers in this book originate from lectures which were held at the "Vienna Workshop on Nonlinear Models and Analysis" – May 20–24, 2002. They represent a cross-section of the research field Applied Nonlinear Analysis with emphasis on free boundaries, fully nonlinear partial differential equations, variational methods, quasilinear partial differential equations and nonlinear kinetic models.

Author: Mimmo Iannelli
Publisher: Springer Science & Business Media
ISBN: 364211069X
Category : Mathematics
Languages : en
Pages : 361

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K.L. Cooke: Delay differential equations.- J.M. Cushing: Volterra integrodifferential equations in population dynamics.- K.P. Hadeler: Diffusion equations in biology.- S. Hastings: Some mathematical problems arising in neurobiology.- F.C. Hoppensteadt: Perturbation methods in biology.- S.O. Londen: Integral equations of Volterra type.

Author: D. S. Jones
Publisher: Springer
ISBN: 9789401159708
Category : Science
Languages : en
Pages : 0

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Book Description
Over the past decade, mathematics has made a considerable impact as a tool with which to model and understand biological phenomena. In return, biology has confronted the mathematician with a variety of challenging problems which have stimulated developments in the theory of nonlinear differential equations. This book is the outcome of the need to introduce undergraduates of mathematics, the physical and biological sciences to some of those developments. It is primarily directed towards students with a mathematical background up to and including that normally taught in a first-year physical science degree of a British university (sophomore year in a North American university) who are interested in the application of mathematics to biological and physical situations. Chapter 1 is introductory, showing how the study of first-order ordinary differential equations may be used to model the growth of a population, monitoring the administration of drugs and the mechanism by which living cells divide. In Chapter 2, a fairly comprehensive account of linear ordinary differential equations with constant coefficients is given. Such equations arise frequently in the discussion of the biological models encountered throughout the text. Chapter 3 is devoted to modelling biological pheno mena and in particular includes (i) physiology of the heart beat cycle, (ii) blood flow, (iii) the transmission of electrochemical pulses in the nerve, (iv) the Belousov-Zhabotinskii chemical reaction and (v) predator-prey models.

Author: T. A. Burton
Publisher: CRC Press
ISBN: 9780824771331
Category : Mathematics
Languages : en
Pages : 300

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Book Description
Persistence in lotka-volterra models of food chains and competition; Mathematical models of humoral immune response; Mathematical models of dose and cell cycle effects in multifraction radiotherapy; Theorical and experimental investigations of microbial competition in continuous culture; A liapunov functional for a class of reaction-diffusion systems; Stochastic prey-predator relationships; Coexistence in predator-prey systems; Stability of some multispecies population models; Population dynamics in patchy environments; Limit cycles in a model of b-cell simulation; Optimal age-specific harvesting policy for a cintinuous time-population model; Models involving differential and integral equations appropriate for describing a temperature dependent predator-prey mite ecosystem on apples.

Author: Jerome A. Goldstein
Publisher: Routledge
ISBN: 1351455184
Category : Mathematics
Languages : en
Pages : 353

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Book Description
Suitable as a textbook for a graduate seminar in mathematical modelling, and as a resource for scientists in a wide range of disciplines. Presents 22 lectures from an international conference in Leibnitz, Austria (no date mentioned), explaining recent developments and results in differential equatio

Author: D. S. Jones
Publisher: Springer
ISBN: 9789401159722
Category : Science
Languages : en
Pages : 340

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Book Description
Over the past decade, mathematics has made a considerable impact as a tool with which to model and understand biological phenomena. In return, biology has confronted the mathematician with a variety of challenging problems which have stimulated developments in the theory of nonlinear differential equations. This book is the outcome of the need to introduce undergraduates of mathematics, the physical and biological sciences to some of those developments. It is primarily directed towards students with a mathematical background up to and including that normally taught in a first-year physical science degree of a British university (sophomore year in a North American university) who are interested in the application of mathematics to biological and physical situations. Chapter 1 is introductory, showing how the study of first-order ordinary differential equations may be used to model the growth of a population, monitoring the administration of drugs and the mechanism by which living cells divide. In Chapter 2, a fairly comprehensive account of linear ordinary differential equations with constant coefficients is given. Such equations arise frequently in the discussion of the biological models encountered throughout the text. Chapter 3 is devoted to modelling biological pheno mena and in particular includes (i) physiology of the heart beat cycle, (ii) blood flow, (iii) the transmission of electrochemical pulses in the nerve, (iv) the Belousov-Zhabotinskii chemical reaction and (v) predator-prey models.

Author: Richard H. Enns
Publisher: Springer Science & Business Media
ISBN: 146844106X
Category : Science
Languages : en
Pages : 609

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Book Description
The Advanced Study Institute (ASI) on Nonlinear Phenomena-in Physics and Biology was held at the Banff Centre, Banff, Alberta, Canada, from 17 - 29 August, 1980. The Institute was made possible through funding by the North Atlantic Treaty Organization (who sup plied the major portion of the financial aid), the National Research and Engineering Council of Canada, and Simon Fraser University. The availability of the Banff Centre was made possible through the co sponsorship (with NATO) of the ASI by the Canadian Association of Physicists. 12 invited lecturers and 82 other participants attended the Institute. Except for two lectures on nonlinear waves by Norman Zabusky, which were omitted because it was felt that they already had been exhaustively treated in the available literature, this volume contains the entire text of the invited lectures. In addition, short reports on some of the contributed talks have also been included. The rationale for the ASI and this resulting volume was that many of the hardest problems and most interesting phenomena being studied by scientists today ar.e nonlinear in nature. The nonlinear models involved often span several different disciplines, °a simple example being the Volterra-type model in population dynamics which has its analogue in nonlinear optics and plasma physics (the 3-wave problem), in the discussion of the social behavior of animals, and in biological competition and selection at the molecular level.

Author: Paul Edgar Phillipson
Publisher: World Scientific
ISBN: 9814271608
Category : Mathematics
Languages : en
Pages : 238

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Book Description
This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions. Sample Chapter(s). Chapter 1: Theme and Contents of this Book (85 KB). Contents: Theme and Contents of this Book; Processes in closed and Open Systems; Dynamics of Molecular Evolution; Relaxation Oscillations; Order and Chaos; Reaction Diffusion Dynamics; Solitons; Neuron Pulse Propagation; Time Reversal, Dissipation and Conservation. Readership: Advanced undergraduates, graduate students and researchers in physics, chemistry, biology or bioinformatics who are interested in mathematical modeling.