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The chemostat is a basic piece of laboratory apparatus, yet it has occupied an increasingly central role in ecological studies. The ecological environment created by a chemostat is one of the few completely controlled experimental systems for testing microbial growth and competition. As a tool in biotechnology, the chemostat plays an important role in bioprocessing. This book presents the theory of the chemostat as a model for larger ecological problems such as food chains, competition along a gradient, competition in the presence of an inhibitor, and the effects of time varying inputs. Models which take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modelled and analysed using the dynamical systems approach. Directions for research and open problems are discussed. Six appendices provide an elementary description of the necessary mathematical tools. Teachers, researchers, and students in applied mathematics, chemical engineering and ecology will find this book a welcome resource.

Microbial growth --- Chemostat. --- Microbial ecology --- Mathematical models.

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Mathematical modeling in the biological sciences is growing exponentially because the general area provides exciting problems from biology to medicine, and this goes under the name mathematical biology. Moreover, models of the growth of microorganisms have become very popular since mathematical predictions can be tested in the laboratory employing a device known as the chemostat. Such models are called chemostat models. This book attempts to present a self contained account of mathematical model building theory of microbial populations. Key Features: Covers all fundamental concepts and mathematical skills needed to build models for microbial populations. Provides an accessible and informative over view of known literature including several practical techniques. Presents a comprehensive analysis of chemostat models and their limitations in adapting to natural lakes. A thorough discussion on the design of biologically viable control mechanisms (termed bio-control mechanisms) to contain the instability tendencies. Construction of a variety of Lyapunov functionals for global stability analysis. This book is ideal for a general scientific and engineering audience requiring an in-depth exposure to current ideas, methods and models. The topics discussed can serve as a one to two semester course material for senior under graduate and graduate students. It is a useful reference for practitioners, researchers, and professionals in applied mathematics, biology, agriculture, limnology, chemical and civil engineering.

Biological systems -- Mathematical models. --- Chemostat. --- Microbial populations -- Mathematical models. --- Microbiological Processes. --- Models, Biological. --- Biological systems --- Microbial populations --- Chemostat --- Epidemiologic Measurements --- Models, Theoretical --- Investigative Techniques --- Microbiological Phenomena --- Statistics as Topic --- Phenomena and Processes --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Public Health --- Epidemiologic Methods --- Environment and Public Health --- Health Care --- Biometry --- Microbiological Processes --- Models, Biological --- Methods --- Biology --- Health & Biological Sciences --- Biology - General --- Mathematical models --- Biomathematics. --- Computational biology. --- Mathematics --- Life sciences. --- Systems biology. --- Microbial ecology. --- Community ecology, Biotic. --- Ecology. --- Life Sciences. --- Systems Biology. --- Mathematical and Computational Biology. --- Theoretical Ecology/Statistics. --- Community & Population Ecology. --- Microbial Ecology. --- Bioinformatics --- Biological models. --- Balance of nature --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Environmental microbiology --- Microorganisms --- Ecology --- Microbiology --- Ecology . --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Computational biology --- Molecular biology --- Biological systems - Mathematical models --- Microbial populations - Mathematical models

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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.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal

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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.

Research & information: general --- Mathematics & science --- cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal