Download or read book Partial Differential Equations in Ecology written by Sergei Petrovski and published by MDPI. This book was released on 2021-03-17 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Parabolic Equations in Biology written by Benoît Perthame and published by Springer. This book was released on 2015-09-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Download or read book Dynamical Systems Bifurcation Analysis and Applications written by Mohd Hafiz Mohd and published by Springer Nature. This book was released on 2019-10-11 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of ​Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop. This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.

Download or read book Stochastic Partial Differential Equations written by Étienne Pardoux and published by Springer Nature. This book was released on 2021-10-25 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a concise introduction to the classical theory of stochastic partial differential equations (SPDEs). It begins by describing the classes of equations which are studied later in the book, together with a list of motivating examples of SPDEs which are used in physics, population dynamics, neurophysiology, finance and signal processing. The central part of the book studies SPDEs as infinite-dimensional SDEs, based on the variational approach to PDEs. This extends both the classical Itô formulation and the martingale problem approach due to Stroock and Varadhan. The final chapter considers the solution of a space-time white noise-driven SPDE as a real-valued function of time and (one-dimensional) space. The results of J. Walsh's St Flour notes on the existence, uniqueness and Hölder regularity of the solution are presented. In addition, conditions are given under which the solution remains nonnegative, and the Malliavin calculus is applied. Lastly, reflected SPDEs and their connection with super Brownian motion are considered. At a time when new sophisticated branches of the subject are being developed, this book will be a welcome reference on classical SPDEs for newcomers to the theory.

Download or read book Mathematical Modeling in Economics Ecology and the Environment written by N.V. Hritonenko and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ...

Download or read book Systems of Nonlinear Partial Differential Equations written by Anthony Leung and published by Springer. This book was released on 1989-04-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.

Download or read book Introduction to Partial Differential Equations written by Aslak Tveito and published by Springer Science & Business Media. This book was released on 2008-01-21 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.

Download or read book Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA written by Elias T. Krainski and published by CRC Press. This book was released on 2018-12-07 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Download or read book Encyclopedia of Theoretical Ecology written by Alan Hastings and published by Univ of California Press. This book was released on 2012-05-31 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A bold and successful attempt to illustrate the theoretical foundations of all of the subdisciplines of ecology, including basic and applied, and extending through biophysical, population, community, and ecosystem ecology. Encyclopedia of Theoretical Ecology is a compendium of clear and concise essays by the intellectual leaders across this vast breadth of knowledge."--Harold Mooney, Stanford University "A remarkable and indispensable reference work that also is flexible enough to provide essential readings for a wide variety of courses. A masterful collection of authoritative papers that convey the rich and fundamental nature of modern theoretical ecology."--Simon A. Levin, Princeton University "Theoretical ecologists exercise their imaginations to make sense of the astounding complexity of both real and possible ecosystems. Imagining a real or possible topic left out of the Encyclopedia of Theoretical Ecology has proven just as challenging. This comprehensive compendium demonstrates that theoretical ecology has become a mature science, and the volume will serve as the foundation for future creativity in this area."--Fred Adler, University of Utah "The editors have assembled an outstanding group of contributors who are a great match for their topics. Sometimes the author is a key, authoritative figure in a field; and at other times, the author has enough distance to convey all sides of a subject. The next time you need to introduce ecology students to a theoretical topic, you'll be glad to have this encyclopedia on your bookshelf."--Stephen Ellner, Cornell University “Everything you wanted to know about theoretical ecology, and much that you didn’t know you needed to know but will now! Alan Hastings and Louis Gross have done us a great service by bringing together in very accessible form a huge amount of information about a broad, complicated, and expanding field.”--Daniel Simberloff, University of Tennessee, Knoxville

Download or read book Applied Partial Differential Equations written by J. David Logan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems;' The audience usually consists of stu dents in mathematics, engineering, and the physical sciences. The topics include derivations of some of the standard equations of mathemati cal physics (including the heat equation, the· wave equation, and the Laplace's equation) and methods for solving those equations on bounded and unbounded domains. Methods include eigenfunction expansions or separation of variables, and methods based on Fourier and Laplace transforms. Prerequisites include calculus and a post-calculus differential equations course. There are several excellent texts for this course, so one can legitimately ask why one would wish to write another. A survey of the content of the existing titles shows that their scope is broad and the analysis detailed; and they often exceed five hundred pages in length. These books gen erally have enough material for two, three, or even four semesters. Yet, many undergraduate courses are one-semester courses. The author has often felt that students become a little uncomfortable when an instructor jumps around in a long volume searching for the right topics, or only par tially covers some topics; but they are secure in completely mastering a short, well-defined introduction. This text was written to proVide a brief, one-semester introduction to partial differential equations.

Download or read book Differential Equations and Applications in Ecology Epidemics and Population Problems written by Stavros Busenberg and published by Elsevier. This book was released on 2012-12-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Download or read book Differential Equations Models in Biology Epidemiology and Ecology written by Stavros Busenberg and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Solving Differential Equations in R written by Karline Soetaert and published by Springer Science & Business Media. This book was released on 2012-06-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Download or read book Elements of Mathematical Ecology written by Mark Kot and published by Cambridge University Press. This book was released on 2001-07-19 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.

Download or read book Nonlinear Physics of Ecosystems written by Ehud Meron and published by CRC Press. This book was released on 2015-04-15 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Physics of Ecosystems introduces the concepts and tools of pattern formation theory and demonstrates their utility in ecological research using problems from spatial ecology. Written in language understandable to both physicists and ecologists in most parts, the book reveals the mechanisms of pattern formation and pattern dynamics. It als

Download or read book Transport Equations in Biology written by Benoît Perthame and published by Springer Science & Business Media. This book was released on 2006-12-14 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.