Reaction Diffusion Equations And Their Applications To Biology
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Reaction Diffusion Equations And Their Applications To Biology
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Author : N. F. Britton
language : en
Publisher:
Release Date : 1986
Reaction Diffusion Equations And Their Applications To Biology written by N. F. Britton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
Although the book is largely self-contained, some knowledge of the mathematics of differential equations is necessary. Thus the book is intended for mathematicians who are interested in the application of their subject to the biological sciences and for biologists with some mathematical training. It is also suitable for postgraduate mathematics students and for undergraduate mathematicians taking a course in mathematical biology. Increasing use of mathematics in developmental biology, ecology, physiology, and many other areas in the biological sciences has produced a need for a complete, mathematical reference for laboratory practice. In this volume, biological scientists will find a rich resource of interesting applications and illustrations of various mathematical techniques that can be used to analyze reaction-diffusion systems. Concepts covered here include:**systems of ordinary differential equations**conservative systems**the scalar reaction-diffusion equation**analytic techniques for systems of parabolic partial differential equations**bifurcation theory**asymptotic methods for oscillatory systems**singular perturbations**macromolecular carriers -- asymptotic techniques.
Parabolic Equations In Biology
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Author : Benoît Perthame
language : en
Publisher: Springer
Release Date : 2015-09-09
Parabolic Equations In Biology written by Benoît Perthame and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
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.
Essential Mathematical Biology
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Author : Nicholas Britton
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-16
Essential Mathematical Biology written by Nicholas Britton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-16 with Mathematics categories.
This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.
A Closer Look Of Nonlinear Reaction Diffusion Equations
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Author : L. Rajendran
language : en
Publisher: Nova Science Publishers
Release Date : 2020-08-26
A Closer Look Of Nonlinear Reaction Diffusion Equations written by L. Rajendran and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-26 with Reaction-diffusion equations categories.
By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area.Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science.This book contains seven chapters and practical applications to the problems of the real world. The first chapter is specifically for those with limited mathematical background. Chapter one presents the introduction of non-linear reaction-diffusion systems, various boundary conditions and examples. Real-life application of non-linear reaction-diffusion in different fields with some important non-linear equations is also discussed. In Chapter 2, mathematical preliminaries and various advanced methods of solving non-linear differential equations such as Homotopy perturbation method, variational iteration method, exponential function method etc. are described with examples.Steady and non-steady state reaction-diffusion equations in the plane sheet (chapter 3), cylinder (chapter 4) and spherical (chapter 5) are analyzed. The analytical results published by various researchers in referred journals during 2007-2020 have been addressed in these chapters 4 to 6, and this leads to conclusions and recommendations on what approaches to use on non-linear reaction-diffusion equations.Convection-diffusion problems arise very often in applied sciences and engineering. Non-linear convection-diffusion equations and corresponding analytical solutions in various fields of chemical sciences are discussed in chapter6. Numerical methods are used to provide approximate results for the non-linear problems, and their importance is felt when it is impossible or difficult to solve a given problem analytically. Chapter 7 identifies some of the numerical methods for finding solutions to non-linear differential equations.
Reaction Diffusion Waves
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Author : Arnaud Ducrot
language : en
Publisher: Editions Publibook
Release Date : 2009
Reaction Diffusion Waves written by Arnaud Ducrot and has been published by Editions Publibook this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Differential operators categories.
A Course In Mathematical Biology
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Author : Gerda de Vries
language : en
Publisher: SIAM
Release Date : 2006-07-01
A Course In Mathematical Biology written by Gerda de Vries and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-01 with Mathematics categories.
This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.
Nonlinear Reaction Diffusion Systems
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Author : Roman Cherniha
language : en
Publisher: Springer
Release Date : 2017-09-18
Nonlinear Reaction Diffusion Systems written by Roman Cherniha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Mathematics categories.
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.
Mathematical Modeling Of Biofilms
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Author : IWA Task Group on Biofilm Modeling
language : en
Publisher: IWA Publishing
Release Date : 2006-04-30
Mathematical Modeling Of Biofilms written by IWA Task Group on Biofilm Modeling and has been published by IWA Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-30 with Science categories.
Over 90% of bacterial biomass exists in the form of biofilms. The ability of bacteria to attach to surfaces and to form biofilms often is an important competitive advantage for them over bacteria growing in suspension. Some biofilms are "good" in natural and engineered systems; they are responsible for nutrient cycling in nature and are used to purify waters in engineering processes. Other biofilms are "bad" when they cause fouling and infections of humans and plants. Whether we want to promote good biofilms or eliminate bad biofilms, we need to understand how they work and what works to control them. Mathematical Modeling of Biofilms provides guidelines for the selection and use of mathematical models of biofilms. The whole range of existing models - from simple analytical expressions to complex numerical models - is covered. The application of the models for the solution of typical problems is demonstrated, and the performance of the models is tested in comparative studies. With the dramatic evolution of the computational capacity still going on, modeling tools for research and practice will become more and more significant in the next few years. This report provides the foundation to understand the models and to select the most appropriate one for a given use. Mathematical Modeling of Biofilms gives a state-of-the-art overview that is especially valuable for educating students, new biofilm researchers, and design engineers. Through a series of three benchmark problems, the report demonstrates how to use the different models and indicates when simple or highly complex models are most appropriate. This is the first report to give a quantitative comparison of existing biofilm models. The report supports model-based design of biofilm reactors. The report can be used as basis for teaching biofilm-system modeling. The report provides the foundation for researchers seeking to use biofilm modeling or to develop new biofilm models. Scientific and Technical Report No.18
Differential Equations With Applications To Biology
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Author : Shigui Ruan
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Differential Equations With Applications To Biology written by Shigui Ruan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.
The Dynamics Of Biological Systems
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Author : Arianna Bianchi
language : en
Publisher: Springer Nature
Release Date : 2019-10-02
The Dynamics Of Biological Systems written by Arianna Bianchi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-02 with Mathematics categories.
The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.