Dynamical Systems In Population Biology

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Dynamical Systems in Population Biology

Xiao-Qiang Zhao
Dynamical Systems in Population Biology Book PDF

Author : Xiao-Qiang Zhao
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 53,7 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780387217611

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Dynamical Systems in Population Biology by Xiao-Qiang Zhao Pdf

Population dynamics is an important subject in mathematical biology. A cen tral problem is to study the long-term behavior of modeling systems. Most of these systems are governed by various evolutionary equations such as difference, ordinary, functional, and partial differential equations (see, e. g. , [165, 142, 218, 119, 55]). As we know, interactive populations often live in a fluctuating environment. For example, physical environmental conditions such as temperature and humidity and the availability of food, water, and other resources usually vary in time with seasonal or daily variations. Therefore, more realistic models should be nonautonomous systems. In particular, if the data in a model are periodic functions of time with commensurate period, a periodic system arises; if these periodic functions have different (minimal) periods, we get an almost periodic system. The existing reference books, from the dynamical systems point of view, mainly focus on autonomous biological systems. The book of Hess [106J is an excellent reference for periodic parabolic boundary value problems with applications to population dynamics. Since the publication of this book there have been extensive investigations on periodic, asymptotically periodic, almost periodic, and even general nonautonomous biological systems, which in turn have motivated further development of the theory of dynamical systems. In order to explain the dynamical systems approach to periodic population problems, let us consider, as an illustration, two species periodic competitive systems dUI dt = !I(t,Ul,U2), (0.

Dynamical Systems and Their Applications in Biology

Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu
Dynamical Systems and Their Applications in Biology Book PDF

Author : Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 53,6 Mb
Release : 2003
Category : Science
ISBN : 9780821831632

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Dynamical Systems and Their Applications in Biology by Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu Pdf

This volume is based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). It presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology. The book contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology. The material is suitable for graduate students and research mathematicians interested in ordinary differential equations and their applications in biology. Also available by Ruan, Wolkowicz, and Wu is Differential Equations with Applications to Biology, Volume 21 in the AMS series Fields Institute Communications.

Current Trends in Dynamical Systems in Biology and Natural Sciences

Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino
Current Trends in Dynamical Systems in Biology and Natural Sciences Book PDF

Author : Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino
Publisher : Springer Nature
Page : 250 pages
File Size : 42,5 Mb
Release : 2020-05-06
Category : Mathematics
ISBN : 9783030411206

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Current Trends in Dynamical Systems in Biology and Natural Sciences by Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino Pdf

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.

Competition Models in Population Biology

Paul Waltman
Competition Models in Population Biology Book PDF

Author : Paul Waltman
Publisher : SIAM
Page : 82 pages
File Size : 45,9 Mb
Release : 1983-01-01
Category : Technology & Engineering
ISBN : 1611970253

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Competition Models in Population Biology by Paul Waltman Pdf

This book uses fundamental ideas in dynamical systems to answer questions of a biologic nature, in particular, questions about the behavior of populations given a relatively few hypotheses about the nature of their growth and interaction. The principal subject treated is that of coexistence under certain parameter ranges, while asymptotic methods are used to show competitive exclusion in other parameter ranges. Finally, some problems in genetics are posed and analyzed as problems in nonlinear ordinary differential equations.

Dynamical Systems and Population Persistence

Hal L. Smith,Horst R. Thieme
Dynamical Systems and Population Persistence Book PDF

Author : Hal L. Smith,Horst R. Thieme
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 46,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821849453

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Dynamical Systems and Population Persistence by Hal L. Smith,Horst R. Thieme Pdf

Providing a self-contained treatment of persistence theory that is accessible to graduate students, this monograph includes chapters on infinite-dimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an age-structured model of cells growing in a chemostat.

Dynamical Systems for Biological Modeling

Fred Brauer,Christopher Kribs
Dynamical Systems for Biological Modeling Book PDF

Author : Fred Brauer,Christopher Kribs
Publisher : CRC Press
Page : 482 pages
File Size : 45,6 Mb
Release : 2015-12-23
Category : Mathematics
ISBN : 9781498774048

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Dynamical Systems for Biological Modeling by Fred Brauer,Christopher Kribs Pdf

Dynamical Systems for Biological Modeling: An Introduction prepares both biology and mathematics students with the understanding and techniques necessary to undertake basic modeling of biological systems. It achieves this through the development and analysis of dynamical systems.The approach emphasizes qualitative ideas rather than explicit computa

Complex Population Dynamics

Peter Turchin
Complex Population Dynamics Book PDF

Author : Peter Turchin
Publisher : Princeton University Press
Page : 471 pages
File Size : 52,7 Mb
Release : 2013-02-15
Category : Science
ISBN : 9781400847280

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Complex Population Dynamics by Peter Turchin Pdf

Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.

Dynamical Systems in Population Biology

Xiao-Qiang Zhao
Dynamical Systems in Population Biology Book PDF

Author : Xiao-Qiang Zhao
Publisher : Springer
Page : 413 pages
File Size : 40,6 Mb
Release : 2017-04-11
Category : Mathematics
ISBN : 9783319564333

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Dynamical Systems in Population Biology by Xiao-Qiang Zhao Pdf

This research monograph provides an introduction to the theory of nonautonomous semiflows with applications to population dynamics. It develops dynamical system approaches to various evolutionary equations such as difference, ordinary, functional, and partial differential equations, and pays more attention to periodic and almost periodic phenomena. The presentation includes persistence theory, monotone dynamics, periodic and almost periodic semiflows, basic reproduction ratios, traveling waves, and global analysis of prototypical population models in ecology and epidemiology. Research mathematicians working with nonlinear dynamics, particularly those interested in applications to biology, will find this book useful. It may also be used as a textbook or as supplementary reading for a graduate special topics course on the theory and applications of dynamical systems. Dr. Xiao-Qiang Zhao is a University Research Professor at Memorial University of Newfoundland, Canada. His main research interests involve applied dynamical systems, nonlinear differential equations, and mathematical biology. He is the author of more than 100 papers, and his research has played an important role in the development of the theory and applications of monotone dynamical systems, periodic and almost periodic semiflows, uniform persistence, and basic reproduction ratios.

Dynamical Systems and Their Applications in Biology

Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu,Fields Institute for Research in Mathematical Sciences
Dynamical Systems and Their Applications in Biology Book PDF

Author : Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu,Fields Institute for Research in Mathematical Sciences
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 45,5 Mb
Release : 2003-01-01
Category : Science
ISBN : 0821871420

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Dynamical Systems and Their Applications in Biology by Shigui Ruan,Gail Susan Kohl Wolkowicz,Jianhong Wu,Fields Institute for Research in Mathematical Sciences Pdf

This volume is based on the proceedings of the International Workshop on Dynamical Systems and their Applications in Biology held at the Canadian Coast Guard College on Cape Breton Island (Nova Scotia, Canada). It presents a broad picture of the current research surrounding applications of dynamical systems in biology, particularly in population biology. The book contains 19 papers and includes articles on the qualitative and/or numerical analysis of models involving ordinary, partial, functional, and stochastic differential equations. Applications include epidemiology, population dynamics, and physiology. The material is suitable for graduate students and research mathematicians interested in ordinary differential equations and their applications in biology. Also available by Ruan, Wolkowicz, and Wu is Differential Equations with Applications to Biology, Volume 21 in the AMS series Fields Institute Communications.

Mathematical Ecology of Populations and Ecosystems

John Pastor
Mathematical Ecology of Populations and Ecosystems Book PDF

Author : John Pastor
Publisher : John Wiley & Sons
Page : 358 pages
File Size : 52,7 Mb
Release : 2011-08-31
Category : Science
ISBN : 9781444358452

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Mathematical Ecology of Populations and Ecosystems by John Pastor Pdf

MATHEMATICAL ECOLOGY Population ecologists study how births and deaths affect the dynamics of populations and communities, while ecosystem ecologists study how species control the flux of energy and materials through food webs and ecosystems. Although all these processes occur simultaneously in nature, the mathematical frameworks bridging the two disciplines have developed independently. Consequently, this independent development of theory has impeded the cross-fertilization of population and ecosystem ecology. Using recent developments from dynamical systems theory, this advanced undergraduate/graduate level textbook shows how to bridge the two disciplines seamlessly. The book shows how bifurcations between the solutions of models can help understand regime shifts in natural populations and ecosystems once thresholds in rates of births, deaths, consumption, competition, nutrient inputs, and decay are crossed. Mathematical Ecology is essential reading for students of ecology who have had a first course in calculus and linear algebra or students in mathematics wishing to learn how dynamical systems theory can be applied to ecological problems.

Nonlinear Dynamics of Interacting Populations

A. D. Bazykin,Aleksandr Iosifovich Khibnik,Bernd Krauskopf
Nonlinear Dynamics of Interacting Populations Book PDF

Author : A. D. Bazykin,Aleksandr Iosifovich Khibnik,Bernd Krauskopf
Publisher : World Scientific
Page : 224 pages
File Size : 47,7 Mb
Release : 1998
Category : Science
ISBN : 9810216858

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Nonlinear Dynamics of Interacting Populations by A. D. Bazykin,Aleksandr Iosifovich Khibnik,Bernd Krauskopf Pdf

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.

Population Dynamics: Algebraic And Probabilistic Approach

Utkir A Rozikov
Population Dynamics Algebraic And Probabilistic Approach Book PDF

Author : Utkir A Rozikov
Publisher : World Scientific
Page : 458 pages
File Size : 51,5 Mb
Release : 2020-04-22
Category : Science
ISBN : 9789811211249

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Population Dynamics: Algebraic And Probabilistic Approach by Utkir A Rozikov Pdf

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.

Complex Population Dynamics

Peter Turchin
Complex Population Dynamics Book PDF

Author : Peter Turchin
Publisher : Princeton University Press
Page : 470 pages
File Size : 41,7 Mb
Release : 2003-02-02
Category : Science
ISBN : 9780691090214

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Complex Population Dynamics by Peter Turchin Pdf

Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.

Mathematics for Ecology and Environmental Sciences

Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato
Mathematics for Ecology and Environmental Sciences Book PDF

Author : Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 44,5 Mb
Release : 2007-01-19
Category : Mathematics
ISBN : 9783540344285

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Mathematics for Ecology and Environmental Sciences by Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato Pdf

This volume discusses the rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. It provides a fascinating survey of the theory of dynamical systems in ecology and environmental science. Each chapter introduces students and scholars to the state-of-the-art in an exciting area, presents new results, and inspires future contributions to mathematical modeling in ecology and environmental sciences.

Differential Equations and Applications in Ecology, Epidemics, and Population Problems

Stavros Busenberg
Differential Equations and Applications in Ecology Epidemics and Population Problems Book PDF

Author : Stavros Busenberg
Publisher : Elsevier
Page : 376 pages
File Size : 46,5 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323153423

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Differential Equations and Applications in Ecology, Epidemics, and Population Problems by Stavros Busenberg Pdf

Differential Equations and Applications in Ecology, Epidemics, and Population Problems is composed of papers and abstracts presented at the 1981 research conference on Differential Equations and Applications to Ecology, Epidemics, and Population Problems held at Harvey Mudd College. The reported researches consist of mathematics that is either a direct outgrowth from questions in population biology and biomathematics, or applicable to such questions. The content of this volume are collected in four groups. The first group addresses aspects of population dynamics that involve the interaction between spatial and temporal effects. The second group covers other questions in population dynamics and some other areas of biomathematics. The third group deals with topics in differential and functional differential equations that are continuing to find important applications in mathematical biology. The last group comprises of work on various aspects of differential equations and dynamical systems, not essentially motivated by biological applications. This book is valuable to students and researchers in theoretical biology and biomathematics, as well as to those interested in modern applications of differential equations.