Partial Differential Equations In Ecology

Author : Sergei Petrovski
Publisher : MDPI
Page : 238 pages
File Size : 51,7 Mb
Release : 2021-03-17
Category : Mathematics
ISBN : 9783036502960

Get Book

Partial Differential Equations in Ecology by Sergei Petrovski Pdf

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Author : Sergei Petrovskii
Publisher : Unknown
Page : 238 pages
File Size : 50,6 Mb
Release : 2021
Category : Electronic
ISBN : 3036502971

Get Book

Partial Differential Equations in Ecology by Sergei Petrovskii Pdf

Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.

Author : Stavros Busenberg,Mario Martelli
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 50,9 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9783642456923

Get Book

Differential Equations Models in Biology, Epidemiology and Ecology by Stavros Busenberg,Mario Martelli Pdf

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 : Mark A. Lewis,Sergei V. Petrovskii,Jonathan R. Potts
Publisher : Springer
Page : 362 pages
File Size : 54,5 Mb
Release : 2016-05-05
Category : Mathematics
ISBN : 9783319320434

Get Book

The Mathematics Behind Biological Invasions by Mark A. Lewis,Sergei V. Petrovskii,Jonathan R. Potts Pdf

This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.

Author : Anthony Leung
Publisher : Springer
Page : 409 pages
File Size : 55,6 Mb
Release : 2014-03-14
Category : Mathematics
ISBN : 9401539383

Get Book

Systems of Nonlinear Partial Differential Equations by Anthony Leung Pdf

Author : Thomas G. Hallam,Simon A. Levin
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642698880

Get Book

Mathematical Ecology by Thomas G. Hallam,Simon A. Levin Pdf

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 : Mark Kot
Publisher : Cambridge University Press
Page : 468 pages
File Size : 53,6 Mb
Release : 2001-07-19
Category : Mathematics
ISBN : 0521001501

Get Book

Elements of Mathematical Ecology by Mark Kot Pdf

An introduction to classical and modern mathematical models, methods, and issues in population ecology.

Author : Maira Aguiar,Carlos Braumann,Bob W. Kooi,Andrea Pugliese,Nico Stollenwerk,Ezio Venturino
Publisher : Springer Nature
Page : 250 pages
File Size : 50,7 Mb
Release : 2020-05-06
Category : Mathematics
ISBN : 9783030411206

Get Book

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.

Author : N.V. Hritonenko,Yuri P. Yatsenko
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 41,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781441997333

Get Book

Mathematical Modeling in Economics, Ecology and the Environment by N.V. Hritonenko,Yuri P. Yatsenko Pdf

The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ...

Author : George F. Oster,Edward O. Wilson
Publisher : Princeton University Press
Page : 300 pages
File Size : 54,8 Mb
Release : 1978
Category : Mathematics
ISBN : 0691082138

Get Book

Seminar on Singularities of Solutions of Linear Partial Differential Equations by George F. Oster,Edward O. Wilson Pdf

Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.

Author : Natali Hritonenko,Yuri Yatsenko
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 43,5 Mb
Release : 2014-01-08
Category : Mathematics
ISBN : 9781461493112

Get Book

Mathematical Modeling in Economics, Ecology and the Environment by Natali Hritonenko,Yuri Yatsenko Pdf

Updated to textbook form by popular demand, this second edition discusses diverse mathematical models used in economics, ecology, and the environmental sciences with emphasis on control and optimization. It is intended for graduate and upper-undergraduate course use, however, applied mathematicians, industry practitioners, and a vast number of interdisciplinary academics will find the presentation highly useful. Core topics of this text are: · Economic growth and technological development · Population dynamics and human impact on the environment · Resource extraction and scarcity · Air and water contamination · Rational management of the economy and environment · Climate change and global dynamics The step-by-step approach taken is problem-based and easy to follow. The authors aptly demonstrate that the same models may be used to describe different economic and environmental processes and that similar investigation techniques are applicable to analyze various models. Instructors will appreciate the substantial flexibility that this text allows while designing their own syllabus. Chapters are essentially self-contained and may be covered in full, in part, and in any order. Appropriate one- and two-semester courses include, but are not limited to, Applied Mathematical Modeling, Mathematical Methods in Economics and Environment, Models of Biological Systems, Applied Optimization Models, and Environmental Models. Prerequisites for the courses are Calculus and, preferably, Differential Equations.

Author : Benoît Perthame
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 49,5 Mb
Release : 2006-12-14
Category : Science
ISBN : 9783764378424

Get Book

Transport Equations in Biology by Benoît Perthame Pdf

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

Author : A.W. Leung
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401539371

Get Book

Systems of Nonlinear Partial Differential Equations by A.W. Leung Pdf

'Et moi ..., si j'avait su comment en reveru.r, One service mathematics has rendered the je n'y scrais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : David F. Parkhurst
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 42,5 Mb
Release : 2007-12-06
Category : Science
ISBN : 9780387342283

Get Book

Introduction to Applied Mathematics for Environmental Science by David F. Parkhurst Pdf

This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. The definition of the structure is presented, followed by additional examples using MATLAB, and analytic methods of solving and learning from the structure.

Author : Sergei V. Petrovskii,Bai-Lian Li
Publisher : CRC Press
Page : 242 pages
File Size : 43,9 Mb
Release : 2005-07-28
Category : Mathematics
ISBN : 1584885211

Get Book

Exactly Solvable Models of Biological Invasion by Sergei V. Petrovskii,Bai-Lian Li Pdf

Much of our current knowledge on biological invasion was derived from field studies, but many recent advances relied heavily on mathematics and computing, particularly mathematical modeling. While numerical simulations are clearly a useful approach, they have some serious drawbacks. Approximations errors and the number of parameter values can have a significant impact on the simulation results, the extent of which often remains obscure. Such difficulties do not arise, however, when the problem can be solved analytically. Exactly Solvable Models of Biological Invasion demonstrates the advantages and methods of obtaining exact solutions of partial differential equations that describe nonlinear problems encountered in the study of invasive species spread. With emphasis on PDEs of diffusion-reaction type, the authors present a comprehensive collection of exactly solvable models and a unified, self-contained description of the relevant mathematical methods. In doing so, they also provide new insight into important issues such as the impact of the Allee effect, the impact of predation, and the interplay between different modes of species dispersal. Full calculation details make this presentation accessible to biologists as well as applied mathematicians, and a range of ecological examples and applications demonstrate the utility of exact methods in practice. Exact solutions provide an immediate, complete description of system dynamics for a wide class of initial conditions and serve as a convenient tool for testing numerical algorithms and codes used in more specialized studies. This book lays the groundwork for bringing the power of exactly solvable models to bear on real-world ecological problems.