Lecture Notes In Biomathematics
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Time Lags In Biological Models
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Author : N. MacDonald
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Time Lags In Biological Models written by N. MacDonald and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Mathematics categories.
In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms.
Methods And Models In Mathematical Biology
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Author : Johannes Müller
language : en
Publisher: Springer
Release Date : 2015-08-13
Methods And Models In Mathematical Biology written by Johannes Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-13 with Mathematics categories.
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
The Dynamics Of Physiologically Structured Populations
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Author : Johan A. Metz
language : en
Publisher: Springer
Release Date : 2014-03-11
The Dynamics Of Physiologically Structured Populations written by Johan A. Metz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-11 with Mathematics categories.
Lindenmayer Systems Fractals And Plants
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Author : Przemyslaw Prusinkiewicz
language : en
Publisher:
Release Date : 2014-01-15
Lindenmayer Systems Fractals And Plants written by Przemyslaw Prusinkiewicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Diffusion Processes And Related Topics In Biology
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Author : Luigi M. Ricciardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Diffusion Processes And Related Topics In Biology written by Luigi M. Ricciardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-13 with Mathematics categories.
These notes are based on a one-quarter course given at the Department of Biophysics and Theoretical Biology of the University of Chicago in 1916. The course was directed to graduate students in the Division of Biological Sciences with interests in population biology and neurobiology. Only a slight acquaintance with probability and differential equations is required of the reader. Exercises are interwoven with the text to encourage the reader to play a more active role and thus facilitate his digestion of the material. One aim of these notes is to provide a heuristic approach, using as little mathematics as possible, to certain aspects of the theory of stochastic processes that are being increasingly employed in some of the population biol ogy and neurobiology literature. While the subject may be classical, the nov elty here lies in the approach and point of view, particularly in the applica tions such as the approach to the neuronal firing problem and its related dif fusion approximations. It is a pleasure to thank Professors Richard C. Lewontin and Arnold J.F. Siegert for their interest and support, and Mrs. Angell Pasley for her excellent and careful typing. I . PRELIMINARIES 1. Terminology and Examples Consider an experiment specified by: a) the experiment's outcomes, ~, forming the space S; b) certain subsets of S (called events) and by the probabilities of these events.
Vito Volterra Symposium On Mathematical Models In Biology
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Author : Claudio Barigozzi
language : en
Publisher:
Release Date : 1980
Vito Volterra Symposium On Mathematical Models In Biology written by Claudio Barigozzi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Biology categories.
Stochastic Biomathematical Models
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Author : Mostafa Bachar
language : en
Publisher: Springer
Release Date : 2012-10-19
Stochastic Biomathematical Models written by Mostafa Bachar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-19 with Mathematics categories.
Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.
Lecture Notes In Biomathematics
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Author : Norman MacDonald
language : en
Publisher:
Release Date : 1974
Lecture Notes In Biomathematics written by Norman MacDonald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Biology categories.
Population Dynamics In Variable Environments
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Author : Shripad Tuljapurkar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Population Dynamics In Variable Environments written by Shripad Tuljapurkar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
Demography relates observable facts about individuals to the dynamics of populations. If the dynamics are linear and do not change over time, the classical theory of Lotka (1907) and Leslie (1945) is the central tool of demography. This book addresses the situation when the assumption of constancy is dropped. In many practical situations, a population will display unpredictable variation over time in its vital rates, which must then be described in statistical terms. Most of this book is concerned with the theory of populations which are subject to random temporal changes in their vital rates, although other kinds of variation (e. g. , cyclical) are also dealt with. The central questions are: how does temporal variation work its way into a population's future, and how does it affect our interpretation of a population's past. The results here are directed at demographers of humans and at popula tion biologists. The uneven mathematical level is dictated by the material, but the book should be accessible to readers interested in population the ory. (Readers looking for background or prerequisites will find much of it in Hal Caswell's Matrix population models: construction, analysis, and in terpretation (Sinauer 1989) ). This book is in essence a progress report and is deliberately brief; I hope that it is not mystifying. I have not attempted to be complete about either the history or the subject, although most sig nificant results and methods are presented.
Lecture Notes In Biomathematics
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Author : Paul C. Fife
language : en
Publisher:
Release Date : 1974
Lecture Notes In Biomathematics written by Paul C. Fife and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Biology categories.