Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. 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. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises.
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.
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.
This book contains the manuscripts of the papers delivered at the International Sym posium on Synergetics held at SchloB Elmau, Bavaria, Germany, from April 30 until May 5, 1979. This conference followed several previous ones (Elmau 1972, Sicily 1974, Elmau 1977). This time the subject of the symposium was "pattern formation by dynam ic systems and pattern recognition". The meeting brought together scientists from such diverse fields as mathematics, physics, chemistry, biology, history as well as experts in the fields of pattern recognition and associative memory. When I started this type of conference in 1972 it appeared to be a daring enter prise. Indeed, we began to explore virgin land of science: the systematic study of cooperative effects in physical systems far from equi~ibrium and in other disciplines. Though these meetings were attended by scientists from quite different disciplines, a basic concept and even a common language were found from the very beginning. The idea that there exist profound analogies in the behaviour of large classes of complex systems, though the systems themselves may be quite different, proved to be most fruitful. I was delighted to see that over the past one or two years quite similar conferences were now held in various places allover the world. The inclusion of prob lems of pattern recognition at the present meeting is a novel feature, however.
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
Takes the hallmarks of metapopulation theory to the next level by considering a group of communities, each of which may contain numerous populations, connected by species interactions within communities and the movement of individuals between communities. This book seeks to understand how communities work in fragmented landscapes.
On Growth and Form Spatio-temporal Pattern Formation in Biology M. A. J. Chaplain and G. D. Singh, both of the University of Dundee, UK J. C. McLachlan, St. Andrews University, UK Spatio-temporal pattern formation is a major area of research within the subject of mathematical biology. The topic involves the use of mathematical modelling to analyse how patterns in biology are created and develop. For example, the growth, over time, of the intricate and beautiful patterns on certain sea-shells or the striped markings on a tiger can be modelled and their development predicted in terms of non-linear mathematical processes. The current volume captures the breadth of recent research into various aspects of spatio-temporal pattern and form, such as development biology, reaction-diffusion systems and morphometrics. * Brings the ideas of the classic On Growth and Form by D'Arcy Thompson, the founding classic of mathematical biology, fully up to date and looks to future developments in the subject * Foreword provided by Professor John Tyler Bonner, Princeton University * World class collection of internationally renowned contributors from both experimental and theoretical backgrounds Taking its inspiration from D'Arcy Thompson's classic and still influential volume On Growth and Form, this new volume presents a collection of 21 articles from the Plenary Speakers of the recent D'Arcy Thompson Conference, held at the University of Dundee, 20-24 September 1998. The topics covered include pattern formation in development biology, reaction-diffusion systems, intercellular systems and morphometrics, offering the reader a stimulating blend of theory and experiment. This book will be of particular interest to bio-mathematicians and development biologists. Paediatric clinicians, evolutionary biologists, orthodontists, anatomists, physiologists and many other members of the biology community will also benefit greatly from it.
Advanced Ecological Theory is intended for both postgraduate students and professional researchers in ecology. It provides an overview of current advances in the field as well as closely related areas in evolution, ecological economics, and natural-resource management, familiarizing the reader with the mathematical, computational and statistical approaches used in these different areas. The book has an exciting set of diverse contributions written by leading authorities.
The essential introduction to population ecology—now expanded and fully updated Ecology is capturing the popular imagination like never before, with issues such as climate change, species extinctions, and habitat destruction becoming ever more prominent. At the same time, the science of ecology has advanced dramatically, growing in mathematical and theoretical sophistication. Here, two leading experts present the fundamental quantitative principles of ecology in an accessible yet rigorous way, introducing students to the most basic of all ecological subjects, the structure and dynamics of populations. John Vandermeer and Deborah Goldberg show that populations are more than simply collections of individuals. Complex variables such as distribution and territory for expanding groups come into play when mathematical models are applied. Vandermeer and Goldberg build these models from the ground up, from first principles, using a broad range of empirical examples, from animals and viruses to plants and humans. They address a host of exciting topics along the way, including age-structured populations, spatially distributed populations, and metapopulations. This second edition of Population Ecology is fully updated and expanded, with additional exercises in virtually every chapter, making it the most up-to-date and comprehensive textbook of its kind. Provides an accessible mathematical foundation for the latest advances in ecology Features numerous exercises and examples throughout Introduces students to the key literature in the field The essential textbook for advanced undergraduates and graduate students An online illustration package is available to professors
This text explores the use of cellular automata in modeling pattern formation in biological systems. It describes several mathematical modeling approaches utilizing cellular automata that can be used to study the dynamics of interacting cell systems both in simulation and in practice. New in this edition are chapters covering cell migration, tissue development, and cancer dynamics, as well as updated references and new research topic suggestions that reflect the rapid development of the field. The book begins with an introduction to pattern-forming principles in biology and the various mathematical modeling techniques that can be used to analyze them. Cellular automaton models are then discussed in detail for different types of cellular processes and interactions, including random movement, cell migration, adhesive cell interaction, alignment and cellular swarming, growth processes, pigment cell pattern formation, tissue development, tumor growth and invasion, and Turing-type patterns and excitable media. In the final chapter, the authors critically discuss possibilities and limitations of the cellular automaton approach in modeling various biological applications, along with future research directions. Suggestions for research projects are provided throughout the book to encourage additional engagement with the material, and an accompanying simulator is available for readers to perform their own simulations on several of the models covered in the text. QR codes are included within the text for easy access to the simulator. With its accessible presentation and interdisciplinary approach, Cellular Automaton Modeling of Biological Pattern Formation is suitable for graduate and advanced undergraduate students in mathematical biology, biological modeling, and biological computing. It will also be a valuable resource for researchers and practitioners in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science. PRAISE FOR THE FIRST EDITION “An ideal guide for someone with a mathematical or physical background to start exploring biological modelling. Importantly, it will also serve as an excellent guide for experienced modellers to innovate and improve their methodologies for analysing simulation results.” —Mathematical Reviews
