Spatial Dynamics And Pattern Formation In Biological Populations
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Spatial Dynamics And Pattern Formation In Biological Populations
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Author : Ranjit Kumar Upadhyay
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2021
Spatial Dynamics And Pattern Formation In Biological Populations written by Ranjit Kumar Upadhyay and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 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.
Spatial Dynamics And Pattern Formation In Biological Populations
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Author : Ranjit Kumar Upadhyay
language : en
Publisher: CRC Press
Release Date : 2021-02-23
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 2021-02-23 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.
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.
Mathematics In Engineering Sciences
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Author : Mangey Ram
language : en
Publisher: CRC Press
Release Date : 2019-09-09
Mathematics In Engineering Sciences written by Mangey Ram and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book includes research studies, novel theory, as well as new methodology and applications in mathematics and management sciences. The book will provide a comprehensive range of mathematics applied to engineering areas for different tasks. It will offer an international perspective and a bridge between classical theory and new methodology in many areas, along with real-life applications. Features Offers solutions to multi-objective transportation problem under cost reliability using utility function Presents optimization techniques to support eco-efficiency assessment in manufacturing processes Covers distance-based function approach for optimal design of engineering processes with multiple quality characteristics Provides discrete time sliding mode control for non-linear networked control systems Discusses second law of thermodynamics as instruments for optimizing fluid dynamic systems and aerodynamic systems
Nonlinear Physics Of Ecosystems
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Author : Ehud Meron
language : en
Publisher: CRC Press
Release Date : 2015-04-15
Nonlinear Physics Of Ecosystems written by Ehud Meron and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-15 with Nature categories.
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
Journal Of Applied Nonlinear Dynamics
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Author : J. A. Tenreiro Machado
language : en
Publisher: L& H Scientific Publishing
Release Date : 2018-07-01
Journal Of Applied Nonlinear Dynamics written by J. A. Tenreiro Machado and has been published by L& H Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-01 with categories.
The interdisciplinary journal publishes original and new research results on Applied Nonlinear Dynamics in science and engineering. The aim of the journal is to stimulate more research interest and attention for nonlinear dynamical behaviors and engineering nonlinearity for design. The manuscripts in complex dynamical systems with nonlinearity and chaos are solicited, which includes physical mechanisms of complex systems and engineering applications of nonlinear dynamics. The journal provides a place to researchers for the rapid exchange of ideas and techniques in nonlinear dynamics and engineering nonlinearity for design. No length limitations for contributions are set, but only concisely written manuscripts are published. Brief papers are published on the basis of Technical Notes. Discussions of previous published papers are welcome. Audience Physicists, Engineers, Mathematicians, Earth and Environmental Scientists involved in Nonlinear Science and Numerical Simulation. Topics of Interest Complex dynamics in engineeringNonlinear vibration and dynamics for designNonlinear dynamical systems and controlFractional dynamics and applicationsChemical dynamics and bio-systemsEconomical dynamics and predictionsDynamical systems synchronizationBio-mechanical systems and devicesNonlinear structural dynamicsNonlinear multi-body dynamicsMultiscale wave propagation in materialsNonlinear rotor dynamicsNonlinear waves and acoustics
Mathematical Studies On Human Disease Dynamics
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Author : Abba B. Gumel
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Mathematical Studies On Human Disease Dynamics written by Abba B. Gumel 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 2006 with Computers categories.
This volume contains the proceedings of the AMS-SIAM-IMS Joint Summer Research Conference on Modeling the Dynamics of Human Diseases: Emerging Paradigms and Challenges, held in Snowbird, Utah, July 17-21, 2005. The goal of the conference was to bring together leading and upcoming researchers to discuss the latest advances and challenges associated with the modeling of the dynamics of emerging and re-emerging diseases, and to explore various control strategies. The articles included in this book are devoted to some of the significant recent advances, trends, and challenges associated with the mathematical modeling and analysis of the dynamics and control of some diseases of public health importance. In addition to illustrating many of the diverse prevailing epidemiological challenges, together with the diversity of mathematical approaches needed to address them, this book provides insights on a number of topical modeling issues such as the modeling and control of mosquito-borne diseases, respiratory diseases, animal diseases (such as foot-and-mouth disease), cancer and tumor growth modeling, influenza, HIV, HPV, rotavirus, etc. This book also touches upon other important topics such as the use of modeling i
Theoretical Approaches To Biological Control
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Author : Bradford A. Hawkins
language : en
Publisher: Cambridge University Press
Release Date : 2008-10-14
Theoretical Approaches To Biological Control written by Bradford A. Hawkins and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-14 with Nature categories.
Biological control is the suppression of pest populations using predators, parasitoids and pathogens. Historically, biological control has largely been on a trial-and-error basis, and has failed more often than it has succeeded. However by developing theories based upon fundamental population principles and the biological characteristics of the pest and agent, we can gain a much better understanding of when and how to use biological control. This book gathers together recent theoretical developments and provides a balanced guide to the important issues that need to be considered in applying ecological theory to biological control. It will be a source of productive and stimulating thought for all those interested in pest management, theoretical ecology and population biology.
Aspects Of Mathematical Modelling
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Author : Roger J. Hosking
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-02
Aspects Of Mathematical Modelling written by Roger J. Hosking 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 2008-03-02 with Mathematics categories.
The construction of mathematical models is an essential scientific activity. Mathematics is associated with developments in science and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in other fields. This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.
Dynamics Of Biological Systems
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Author : Michael Small
language : en
Publisher: CRC Press
Release Date : 2011-08-25
Dynamics Of Biological Systems written by Michael Small and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.
From the spontaneous rapid firing of cortical neurons to the spatial diffusion of disease epidemics, biological systems exhibit rich dynamic behaviour over a vast range of time and space scales. Unifying many of these diverse phenomena, Dynamics of Biological Systems provides the computational and mathematical platform from which to understand the underlying processes of the phenomena. Through an extensive tour of various biological systems, the text introduces computational methods for simulating spatial diffusion processes in excitable media, such as the human heart, as well as mathematical tools for dealing with systems of nonlinear ordinary and partial differential equations, such as neuronal activation and disease diffusion. The mathematical models and computer simulations offer insight into the dynamics of temporal and spatial biological systems, including cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behaviour, the interaction of autonomous agents, and hierarchical and structured network topologies. Tools from complex systems and complex networks are also presented for dealing with real phenomenological systems. With exercises and projects in each chapter, this classroom-tested text shows students how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. MATLAB® implementations of algorithms and case studies are available on the author’s website.