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Author: N Goel
Publisher: Elsevier
ISBN: 032316093X
Category : Science
Languages : en
Pages : 154
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Book Description
On the Volterra and Other Nonlinear Models of Interacting Populations explores the various models brought upon to investigate the different assemblies known to man. Assemblies include populations of various biological species, countries, and political parties among others. Because there are numerous assemblies to be measured and evaluated, it has been decided that a standard model be used to ascertain a detailed investigation. One of the models that have been brought forward is introduced by Volterra, which started as a basis for ecological processes. The book begins by establishing that Volterra's model is one of the simplest nonlinear competition models. It explores the model through the study of the population growth of a species. It also covers other theories and concepts relating to the Volterra model in the context of the study. These include equilibrium theory, diversity and stability in ecological systems, and time lags in population among others. The book is a helpful reference for students, researchers, scientists, policymakers, and other parties in search of model/s that fully investigate different assemblies.
Author: N Goel
Publisher: Elsevier
ISBN: 032316093X
Category : Science
Languages : en
Pages : 154
Get Book Here
Book Description
On the Volterra and Other Nonlinear Models of Interacting Populations explores the various models brought upon to investigate the different assemblies known to man. Assemblies include populations of various biological species, countries, and political parties among others. Because there are numerous assemblies to be measured and evaluated, it has been decided that a standard model be used to ascertain a detailed investigation. One of the models that have been brought forward is introduced by Volterra, which started as a basis for ecological processes. The book begins by establishing that Volterra's model is one of the simplest nonlinear competition models. It explores the model through the study of the population growth of a species. It also covers other theories and concepts relating to the Volterra model in the context of the study. These include equilibrium theory, diversity and stability in ecological systems, and time lags in population among others. The book is a helpful reference for students, researchers, scientists, policymakers, and other parties in search of model/s that fully investigate different assemblies.
Author: A. D. Bazykin
Publisher: World Scientific
ISBN: 9789810216856
Category : Science
Languages : en
Pages : 224
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Book Description
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of “dangerous boundaries” in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics — a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.
Author: Elizabeth Spencer Allman
Publisher: Cambridge University Press
ISBN: 9780521525862
Category : Mathematics
Languages : en
Pages : 388
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Book Description
This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.
Author: Narendra S. Goel
Publisher: Elsevier
ISBN: 1483278107
Category : Science
Languages : en
Pages : 282
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Book Description
Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis.
Author: E. R. Lewis
Publisher: Springer Science & Business Media
ISBN: 3642811345
Category : Mathematics
Languages : en
Pages : 414
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Book Description
This book is an outgrowth of one phase of an upper-division course on quantitative ecology, given each year for the past eight at Berkeley. I am most grateful to the students in that course and to many graduate students in the Berkeley Department of Zoology and Colleges of Engineering and Natural Resources whose spirited discussions inspired much of the book's content. I also am deeply grateful to those faculty colleagues with whom, at one time or another, I have shared courses or seminars in ecology or population biology, D.M. Auslander, L. Demetrius, G. Oster, O.H. Paris, F.A. Pitelka, A.M. Schultz, Y. Takahashi, D.B. Tyler, and P. Vogelhut, all of whom contributed substantially to the development of my thinking in those fields, to my Depart mental colleagues E. Polak and A.J. Thomasian, who guided me into the litera ture on numerical methods and stochastic processes, and to the graduate students who at one time or another have worked with me on population-biology projects, L.M. Brodnax, S-P. Chan, A. Elterman, G.C. Ferrell, D. Green, C. Hayashi, K-L. Lee, W.F. Martin Jr., D. May, J. Stamnes, G.E. Swanson, and I. Weeks, who, together, undoubtedly provided me with the greatest inspiration. I am indebted to the copy-editing and production staff of Springer-Verlag, especially to Ms. M. Muzeniek, for their diligence and skill, and to Mrs. Alice Peters, biomathematics editor, for her patience.
Author: T. A. Burton
Publisher: Routledge
ISBN: 135143103X
Category : Mathematics
Languages : en
Pages : 292
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Book Description
First published in 1980. CRC Press is an imprint of Taylor & Francis.
Author: M. Bazin
Publisher: CRC Press
ISBN: 1351092545
Category : Science
Languages : en
Pages : 329
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Book Description
Physiological Models in Microbiology consists of two volumes. Volume I considers models of basic growth processes and the effects of environmental factors on microbial growth. Volume II describes models of secondary processes, in particular, microbial death, spore germination, chemotaxis, and surface growth.
Author: Maira Aguiar
Publisher: Springer Nature
ISBN: 3030411206
Category : Mathematics
Languages : en
Pages : 250
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Book Description
This book disseminates the latest results and envisages new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology. It comprises a collection of the main results presented at the Ninth Edition of the International Workshop “Dynamical Systems Applied to Biology and Natural Sciences – DSABNS”, held from 7 to 9 February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic application. The topics covered in the 12 peer-reviewed contributions involve such diverse mathematical tools as ordinary and partial differential equations, delay equations, stochastic equations, control, and sensitivity analysis. The book is intended to help both in disseminating the latest results and in envisaging new challenges in the application of mathematics to various practical situations in biology, epidemiology, and ecology.
Author: Thomas G. Hallam
Publisher: Springer Science & Business Media
ISBN: 3642698883
Category : Mathematics
Languages : en
Pages : 455
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Book Description
There isprobably no more appropriate location to hold a course on mathematical ecology than Italy, the countryofVito Volterra, a founding father ofthe subject. The Trieste 1982Autumn Course on Mathematical Ecology consisted of four weeksofvery concentrated scholasticism and aestheticism. The first weeks were devoted to fundamentals and principles ofmathematicalecology. A nucleusofthe material from the lectures presented during this period constitutes this book. The final week and a half of the Course was apportioned to the Trieste Research Conference on Mathematical Ecology whose proceedings have been published as Volume 54, Lecture Notes in Biomathematics, Springer-Verlag. The objectivesofthe first portionofthe course wereambitious and, probably, unattainable. Basic principles of the areas of physiological, population, com munitY, and ecosystem ecology that have solid ecological and mathematical foundations were to be presented. Classical terminology was to be introduced, important fundamental topics were to be developed, some past and some current problems of interest were to be presented, and directions for possible research were to be provided. Due to time constraints, the coverage could not be encyclopedic;many areas covered already have merited treatises of book length. Consequently, preliminary foundation material was covered in some detail, but subject overviewsand area syntheseswerepresented when research frontiers were being discussed. These lecture notes reflect this course philosophy.
Author: John A. Adam
Publisher: Springer Science & Business Media
ISBN: 0817681191
Category : Mathematics
Languages : en
Pages : 357
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Book Description
Mathematical Modeling and Immunology An enormous amount of human effort and economic resources has been directed in this century to the fight against cancer. The purpose, of course, has been to find strategies to overcome this hard, challenging and seemingly endless struggle. We can readily imagine that even greater efforts will be required in the next century. The hope is that ultimately humanity will be successful; success will have been achieved when it is possible to activate and control the immune system in its competition against neoplastic cells. Dealing with the above-mentioned problem requires the fullest pos sible cooperation among scientists working in different fields: biology, im munology, medicine, physics and, we believe, mathematics. Certainly, bi ologists and immunologists will make the greatest contribution to the re search. However, it is now increasingly recognized that mathematics and computer science may well able to make major contributions to such prob lems. We cannot expect mathematicians alone to solve fundamental prob lems in immunology and (in particular) cancer research, but valuable sup port, however modest, can be provided by mathematicians to the research aspirations of biologists and immunologists working in this field.
