Spatial Ecology Via Reaction Diffusion Equations
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Spatial Ecology Via Reaction Diffusion Equations
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Author : Robert Stephen Cantrell
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-09
Spatial Ecology Via Reaction Diffusion Equations written by Robert Stephen Cantrell and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-09 with Mathematics categories.
Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models. * Rapidly expanding area of research for biologists and applied mathematicians * Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models * Provides the reader with the tools needed to construct and interpret models * Offers specific applications of both the models and the methods * Authors have played a dominant role in the field for years Essential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.
Spatial Dynamics And Pattern Formation In Biological Populations
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Author : Ranjit Kumar Upadhyay
language : en
Publisher: CRC Press
Release Date : 2021-02-24
Spatial Dynamics And Pattern Formation In Biological Populations written by Ranjit Kumar Upadhyay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-24 with Mathematics categories.
The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time). Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented. Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.
Integrodifference Equations In Spatial Ecology
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Author : Frithjof Lutscher
language : en
Publisher: Springer Nature
Release Date : 2019-10-30
Integrodifference Equations In Spatial Ecology written by Frithjof Lutscher and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-30 with Mathematics categories.
This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike.
Systems Level Modelling Of Microbial Communities
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Author : Aarthi Ravikrishnan
language : en
Publisher: CRC Press
Release Date : 2018-09-06
Systems Level Modelling Of Microbial Communities written by Aarthi Ravikrishnan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-06 with Computers categories.
Systems-Level Modelling of Microbial Communities: Theory and Practice introduces various aspects of modelling microbial communities and presents a detailed overview of the computational methods which have been developed in this area. This book is aimed at researchers in the field of computational/systems biology as well as biologists/experimentalists studying microbial communities, who are keen on embracing the concepts of computational modelling. The primary focus of this book is on methods for modelling interactions between micro-organisms in a community, with special emphasis on constraint-based and network-based modelling techniques. A brief overview of population- and agent-based modelling is also presented. Lastly, it covers the experimental methods to understand microbial communities, and provides an outlook on how the field may evolve in the coming years.
Elliptic Partial Differential Equations
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Author : Vitaly Volpert
language : en
Publisher: Springer
Release Date : 2014-05-10
Elliptic Partial Differential Equations written by Vitaly Volpert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.
The Mathematics Of Diffusion
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Author : Wei-Ming Ni
language : en
Publisher: SIAM
Release Date : 2011-10-13
The Mathematics Of Diffusion written by Wei-Ming Ni and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka–Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.
Proceedings Wascom 2007 14th Conference On Waves And Stability In Continuous Media
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Author : Roberto Monaco
language : en
Publisher: World Scientific
Release Date : 2008
Proceedings Wascom 2007 14th Conference On Waves And Stability In Continuous Media written by Roberto Monaco and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations.
Mathematical Methods In Engineering And Applied Sciences
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Author : Hemen Dutta
language : en
Publisher: CRC Press
Release Date : 2020-01-03
Mathematical Methods In Engineering And Applied Sciences written by Hemen Dutta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
Recognized as a "Recommended" title by Choice for their October 2020 issue. Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing. This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences. Presents theory, methods, and applications in a balanced manner Includes the basic developments with full details Contains the most recent advances and offers enough references for further study Written in a self-contained style and provides proof of necessary results Offers research problems to help early career researchers prepare research proposals Mathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.
Spatial Simulation
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Author : David O'Sullivan
language : en
Publisher: John Wiley & Sons
Release Date : 2013-09-10
Spatial Simulation written by David O'Sullivan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-10 with Technology & Engineering categories.
A ground-up approach to explaining dynamic spatial modelling for an interdisciplinary audience. Across broad areas of the environmental and social sciences, simulation models are an important way to study systems inaccessible to scientific experimental and observational methods, and also an essential complement to those more conventional approaches. The contemporary research literature is teeming with abstract simulation models whose presentation is mathematically demanding and requires a high level of knowledge of quantitative and computational methods and approaches. Furthermore, simulation models designed to represent specific systems and phenomena are often complicated, and, as a result, difficult to reconstruct from their descriptions in the literature. This book aims to provide a practical and accessible account of dynamic spatial modelling, while also equipping readers with a sound conceptual foundation in the subject, and a useful introduction to the wide-ranging literature. Spatial Simulation: Exploring Pattern and Process is organised around the idea that a small number of spatial processes underlie the wide variety of dynamic spatial models. Its central focus on three ‘building-blocks’ of dynamic spatial models – forces of attraction and segregation, individual mobile entities, and processes of spread – guides the reader to an understanding of the basis of many of the complicated models found in the research literature. The three building block models are presented in their simplest form and are progressively elaborated and related to real world process that can be represented using them. Introductory chapters cover essential background topics, particularly the relationships between pattern, process and spatiotemporal scale. Additional chapters consider how time and space can be represented in more complicated models, and methods for the analysis and evaluation of models. Finally, the three building block models are woven together in a more elaborate example to show how a complicated model can be assembled from relatively simple components. To aid understanding, more than 50 specific models described in the book are available online at patternandprocess.org for exploration in the freely available Netlogo platform. This book encourages readers to develop intuition for the abstract types of model that are likely to be appropriate for application in any specific context. Spatial Simulation: Exploring Pattern and Process will be of interest to undergraduate and graduate students taking courses in environmental, social, ecological and geographical disciplines. Researchers and professionals who require a non-specialist introduction will also find this book an invaluable guide to dynamic spatial simulation.
Partial Differential Equations In Ecology
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Author : Sergei Petrovski
language : en
Publisher: MDPI
Release Date : 2021-03-17
Partial Differential Equations In Ecology written by Sergei Petrovski and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Mathematics categories.
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.