This volume discusses the rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. It provides a fascinating survey of the theory of dynamical systems in ecology and environmental science. Each chapter introduces students and scholars to the state-of-the-art in an exciting area, presents new results, and inspires future contributions to mathematical modeling in ecology and environmental sciences.
This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. The definition of the structure is presented, followed by additional examples using MATLAB, and analytic methods of solving and learning from the structure.
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 ...
Updated to textbook form by popular demand, this second edition discusses diverse mathematical models used in economics, ecology, and the environmental sciences with emphasis on control and optimization. It is intended for graduate and upper-undergraduate course use, however, applied mathematicians, industry practitioners, and a vast number of interdisciplinary academics will find the presentation highly useful. Core topics of this text are: · Economic growth and technological development · Population dynamics and human impact on the environment · Resource extraction and scarcity · Air and water contamination · Rational management of the economy and environment · Climate change and global dynamics The step-by-step approach taken is problem-based and easy to follow. The authors aptly demonstrate that the same models may be used to describe different economic and environmental processes and that similar investigation techniques are applicable to analyze various models. Instructors will appreciate the substantial flexibility that this text allows while designing their own syllabus. Chapters are essentially self-contained and may be covered in full, in part, and in any order. Appropriate one- and two-semester courses include, but are not limited to, Applied Mathematical Modeling, Mathematical Methods in Economics and Environment, Models of Biological Systems, Applied Optimization Models, and Environmental Models. Prerequisites for the courses are Calculus and, preferably, Differential Equations.
This volume contains a cross-section of the papers presented at the International Symposium on Mathematical Modelling of Ecological, Environmental and Biological Systems held in Kanpur, India, in August 1985. The choice of topics emphasizes many aspects of ecological and environmental matters including air and water pollution, ecotoxicology, resource management, epidemiology, and population and community ecology.It is intended that this volume will focus international attention upon some problems in the ecological and environmental sciences that can be impacted by mathematical modelling and analysis.
There isprobably no more appropriate location to hold a course on mathematical ecology than Italy, the countryofVito Volterra, a founding father ofthe subject. The Trieste 1982Autumn Course on Mathematical Ecology consisted of four weeksofvery concentrated scholasticism and aestheticism. The first weeks were devoted to fundamentals and principles ofmathematicalecology. A nucleusofthe material from the lectures presented during this period constitutes this book. The final week and a half of the Course was apportioned to the Trieste Research Conference on Mathematical Ecology whose proceedings have been published as Volume 54, Lecture Notes in Biomathematics, Springer-Verlag. The objectivesofthe first portionofthe course wereambitious and, probably, unattainable. Basic principles of the areas of physiological, population, com munitY, and ecosystem ecology that have solid ecological and mathematical foundations were to be presented. Classical terminology was to be introduced, important fundamental topics were to be developed, some past and some current problems of interest were to be presented, and directions for possible research were to be provided. Due to time constraints, the coverage could not be encyclopedic;many areas covered already have merited treatises of book length. Consequently, preliminary foundation material was covered in some detail, but subject overviewsand area syntheseswerepresented when research frontiers were being discussed. These lecture notes reflect this course philosophy.
This edited volume focuses on how we can protect our environment and enhance environmental sustainability when faced with changes and pressures imposed by our expansive needs. The volume unites multiple subject areas within sustainability, enabling the techniques and philosophy in the chapters to be applied to research areas in environmental science, plant sciences, energy, biodiversity and conservation. The chapters from expert contributors cover topics such as mathematical modelling tools used to monitor diversity of plant species, and the stability of ecosystem services such as biogeochemical cycling. Empirical research presented here also brings together mathematical developments in the important fields of robotics including kinematics, dynamics, path planning, control, vision, and swarmanoids. Through this book readers will also discover about rainfall-runoff modelling which will give them a better idea of the effects of climate change on the sustainability of water resources at the watershed scale. Modelling approaches will also be examined that maximize readers insights into the global problem of energy transition, i.e. the switch to an energy production system using renewable resources only. Collective and discrete insights are made to assist with synergy which should progress well beyond this book. Insight is also given to assist policy formations, development and implementations. The book has a strong multi-disciplinary nature at its core, and will appeal to both generalist readers and specialists in information technology, mathematics, biology, physics, chemistry and environmental sciences.
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.
A thorough revision of the previous "Environmental Engineer's Mathematics Handbook," this book offers readers an unusual approach to presenting environmental math concepts, emphasizing the relationship between the principles in natural processes and environmental processes. It integrates the fundamental math operations performed by environmental pr
New statistical tools are changing the ways in which scientists analyze and interpret data and models. Many of these are emerging as a result of the wide availability of inexpensive, high speed computational power. In particular, hierarchical Bayes and Markov Chain Monte Carlo methods for analysis provide consistent framework for inference and prediction where information is heterogeneous and uncertain, processes are complex, and responses depend on scale. Nowhere are these methods more promising than in the environmental sciences. Models have developed rapidly, and there is now a requirement for a clear exposition of the methodology through to application for a range of environmental challenges.