Download or read book Time Lags in Biological Models written by N. MacDonald and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many biological models it is necessary to allow the rates of change of the variables to depend on the past history, rather than only the current values, of the variables. The models may require discrete lags, with the use of delay-differential equations, or distributed lags, with the use of integro-differential equations. In these lecture notes I discuss the reasons for including lags, especially distributed lags, in biological models. These reasons may be inherent in the system studied, or may be the result of simplifying assumptions made in the model used. I examine some of the techniques available for studying the solution of the equations. A large proportion of the material presented relates to a special method that can be applied to a particular class of distributed lags. This method uses an extended set of ordinary differential equations. I examine the local stability of equilibrium points, and the existence and frequency of periodic solutions. I discuss the qualitative effects of lags, and how these differ according to the choice of discrete or distributed lag. The models studied are drawn from the population dynamiCS of single species (logistic growth, the chemostat) and of interacting pairs of species (predation, mutualism), from cell population dynamiCS (haemopoiesis) and from biochemical kinetics (the Goodwin oscillator). The last chapter is devoted to a population model employing difference equations. All these models include non-linear terms.
Download or read book Biological Delay Systems written by Norman MacDonald and published by Cambridge University Press. This book was released on 2008-01-03 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for delays such as those due to gestation, maturation or transport. This book deals with a fundamental question in the analysis of the effects of delays, namely whether they affect the stability of steady states.
Download or read book Modelling Biological Populations in Space and Time written by Eric Renshaw and published by Cambridge University Press. This book was released on 1993-08-26 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops a unifying approach to population studies, emphasising the interplay between modelling and experimentation. Throughout, mathematicians and biologists are provided with a framework within which population dynamics can be fully explored and understood. Aspects of population dynamics covered include birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. Both deterministic and stochastic models are considered. Whilst the more theoretically orientated sections will appeal to mathematical biologists, the material is presented so that readers with little mathematical expertise can bypass these without losing the main flow of the text.
Download or read book Topics in Mathematical Biology written by Karl Peter Hadeler and published by Springer. This book was released on 2017-12-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in Mathematical Biology general principles about coupled and quiescent systems are derived, including results on shrinking periodic orbits and stabilization of oscillations via quiescence. In subsequent chapters classical biological models are presented in detail and challenged by the introduction of quiescence. These models include delay equations, demographic models, age structured models, Lotka-Volterra systems, replicator systems, genetic models, game theory, Nash equilibria, evolutionary stable strategies, ecological models, epidemiological models, random walks and reaction-diffusion models. In each case we find new and interesting results such as stability of fixed points and/or periodic orbits, excitability of steady states, epidemic outbreaks, survival of the fittest, and speeds of invading fronts. The textbook is intended for graduate students and researchers in mathematical biology who have a solid background in linear algebra, differential equations and dynamical systems. Readers can find gems of unexpected beauty within these pages, and those who knew K.P. (as he was often called) well will likely feel his presence and hear him speaking to them as they read.
Download or read book Mathematical Biology written by James D. Murray and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical biology - the use of mathematical ideas and models in the biosciences - is a fast growing, very exciting and increasingly important inderdisciplinary field. This textbook is an account of some of the major techniques and models used and of some genuine practical applications drawn from current areas of research interest in, for example, population ecology, developmental biology, physiology, epidemiology and evolution. It provides the reader with a thorough background, sufficient to start genuine interdisciplinary collaborative reserach with biomedical scientists.
Download or read book Dynamics of Nonlinear Time Delay Systems written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions. Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics and the detailed presentation of real-world applications.
Download or read book Robust Control and Filtering for Time Delay Systems written by Magdi S. Mahmoud and published by CRC Press. This book was released on 2018-10-08 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of robust control and filtering for time-delay systems. It provides information on approaches to stability, stabilization, control design, and filtering aspects of electronic and computer systems - explicating the developments in time-delay systems and uncertain time-delay systems. There are appendices detailing important facets of matrix theory, standard lemmas and mathematical results, and applications of industry-tested software.
Download or read book Mathematical and Statistical Approaches to AIDS Epidemiology written by Carlos Castillo-Chavez and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 18 research articles of this volume discuss the major themes that have emerged from mathematical and statistical research in the epidemiology of HIV. The opening paper reviews important recent contributions. Five sections follow: Statistical Methodology and Forecasting, Infectivity and the HIV, Heterogeneity and HIV Transmission Dynamics, Social Dynamics and AIDS, and The Immune System and The HIV. In each, leading experts in AIDS epidemiology present the recent results. Some address the role of variable infectivity, heterogeneous mixing, and long periods of infectiousness in the dynamics of HIV; others concentrate on parameter estimation and short-term forecasting. The last section looks at the interaction between the HIV and the immune system.
Download or read book The Dynamics of Physiologically Structured Populations written by Johan A. Metz and published by Springer. This book was released on 2014-03-11 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transient Processes in Cell Proliferation Kinetics written by Andrej Yu. Yakovlev and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematician who has taken the romantic decision to devote himself to biology will doubtlessly look upon cell kinetics as the most simple and natural field of application for his knowledge and skills. Indeed, the thesaurus he is to master is not so complicated as, say, in molecular biology, the structural elements of the system, i. e. ceils, have been segregated by Nature itself, simple considerations of balance may be used for deducing basic equations, and numerous analogies in other areas of science also superficial add to one"s confidence. Generally speaking, this number of impression is correct, as evidenced by the very great theoretical studies on population kinetics, unmatched in other branches of mathematical biology. This, however, does not mean that mathematical theory of cell systems has traversed in its development a pathway free of difficulties or errors. The seeming ease of formalizing the phenomena of cell kinetics not infrequently led to the appearance of mathematical models lacking in adequacy or effectiveness from the viewpoint of applications. As in any other domain of science, mathematical theory of cell systems has its own intrinsic logic of development which, however, depends in large measure on the progress in experimental biology. Thus, during a fairly long period running into decades activities in that sphere were centered on devising its own specific approaches necessitated by new objectives in the experimental in vivo and in vitro investigation of cell population kinetics in different tissues.
Download or read book Depth Perception in Frogs and Toads written by Donald House and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Depth Perception in Frogs and Toads provides a comprehensive exploration of the phenomenon of depth perception in frogs and toads, as seen from a neuro-computational point of view. Perhaps the most important feature of the book is the development and presentation of two neurally realizable depth perception algorithms that utilize both monocular and binocular depth cues in a cooperative fashion. One of these algorithms is specialized for computation of depth maps for navigation, and the other for the selection and localization of a single prey for prey catching. The book is also unique in that it thoroughly reviews the known neuroanatomical, neurophysiological and behavioral data, and then synthesizes, organizes and interprets that information to explain a complex sensory-motor task. The book will be of special interest to that segment of the neural computing community interested in understanding natural neurocomputational structures, particularly to those working in perception and sensory-motor coordination. It will also be of interest to neuroscientists interested in exploring the complex interactions between the neural substrates that underly perception and behavior.
Download or read book An Essay on the Importance of Being Nonlinear written by Bruce J. West and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of my favorite quotes is from a letter of Charles Darwin (1887): "I have long discovered that geologists never read each other's works, and that the only object in writing a book is proof of earnestness, and that you do not form your opinions without undergoing labour of some kind. " It is not clear if this private opinion of Darwin was one that he held to be absolutely true, or was one of those opinions that, as with most of us, coincides with our "bad days," but is replaced with a more optimistic view on our "good days. " I hold the sense of the statement to be true in general, but not with regard to scientists never reading each other's work. Even if that were true however, the present essay. would still have been written as a proof of earnestness. This essay outlines my personal view of how nonlinear mathematics may be of value in formulating models outside the physical sciences. This perspective has developed over a number of years during which time I have repeatedly been amazed at how an "accepted" model would fail to faithfully characterize the full range of avail able data because of its implicit or explicit dependence on linear concepts. This essay is intended to demonstrate how linear ideas have come to dominate and therefore limit a scientist's ability to understand any given class of phenomena.
Download or read book Trees and Hierarchical Structures written by Andreas Dress and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "raison d'etre" of hierarchical dustering theory stems from one basic phe nomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to dassify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping dusters such that any two objects in ~ne duster appear to be more related to each other than they are to objects outside this duster. In everyday life, as well as in essentially every field of scientific investigation, there is an urge to reduce complexity by recognizing and establishing reasonable das sification schemes. Unfortunately, this is counterbalanced by the experience of seemingly unavoidable deadlocks caused by the existence of sequences of objects, each comparatively similar to the next, but the last rather different from the first.
Download or read book Stochastic Processes in Epidemic Theory written by Jean-Pierre Gabriel and published by Springer. This book was released on 2014-03-11 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
Download or read book Population Genetics in Forestry written by Hans-Rolf Gregorius and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: When we consider the main object of forestry, the tree, it immediately becomes clear why experimental population geneticists have been so hesitant in making this object a primary concern of their research. Trees are very long-living organisms with generation intervals frequently exceeding those of their investigators by multiples. They virtually exclude, therefore, application of the classical methods of population genetics since these are based on observing genetic structures over generations. This situation, where the limits set to observation are so severe, particularly requires close cooperation between theory and experiment. It also requires careful consideration of results obtained for organisms other than trees, in order to gain additional insights by comparing the results for trees with those for other organisms. Yet, the greatest challenge to population and ecological genetics probably originates from the fact that forests are very likely to be the most complex ecosystems of all, even in some cases where they are subject to intense management. This complexity, which equally comprises biotic and abiotic factors varying both in time and space, makes extremely high demands on the adaptational capacity and thus flexibility of the carriers of such an ecosystem. Longevity combined with immobility during the vegetative phase, however, appears to contradict the obvious necessity of adaptational flexibility in forest tree populations when compared with short lived and/or mobile organisms.
Download or read book Acanthaster and the Coral Reef A Theoretical Perspective written by Roger H. Bradbury and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In August 1988. the Sixth International Coral Reef Symposium was held in Townsville resulting in an influx of most of the world's coral reef sCientists to the city. We seized this opportunity at the Australian Institute of Marine Science to run a small workshop immediately before the symposium on the outbreaks of the crown-of-thorns starfish. Aeanthaster planei. We invited that small band of mathematicians who had been modelling the phenomenon, (and who may not have normally attended an international meeting so thoroughly dedicated to natural science) to meet with those SCientists who had been been actively working on the phenomenon in the field. John Casti notes in his delightful new book Alternate Realities (Wiley, 1989): 'If the natural role of the experimenter is to generate new observables by which we know the processes of Nature, and the natural role of the mathematician is to generate new formal structures by which we can represent these processes. then the system SCientist finds his niche by serving as a broker between the two. ' I think our book shows the fruits of that brokerage through the wide range of models explored within its pages. the high level of collaboration and interaction across disciplines evident in the individual papers, and in the emerging synthesis that reflects a far deeper understanding of this complex phenomenon than was possible even a few years ago.
Download or read book Mathematical Approaches to Problems in Resource Management and Epidemiology written by Carlos Castillo-Chavez and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Increasingly, mathematical methods are being used to advantage in addressing the problems facing humanity in managing its environment. Problems in resource management and epidemiology especially have demonstrated the utility of quantitative modeling. To explore these approaches, the Center of Applied Mathematics at Cornell University organized a conference in Fall, 1987, with the objective of surveying and assessing the state of the art. This volume records the proceedings of that conference. Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. Cell population growth presents the simplest of systems for study, and is of fundamental importance in its own right for a variety of medical and environmental applications. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth. Together, these provide a valuable introduction to mathematical cell biology.
