[PDF] Spaces Of Measures And Their Applications To Structured Population Models eBook

Author : Christian Düll
Publisher : Cambridge University Press
Page : 321 pages
File Size : 26,90 MB
Release : 2021-10-07
Category : Mathematics
ISBN : 1316519104

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Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.

Author : Horst R. Thieme
Publisher : American Mathematical Society
Page : 357 pages
File Size : 16,37 MB
Release : 2024-05-07
Category : Mathematics
ISBN : 1470474654

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A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

Author : J. M. Cushing
Publisher : SIAM
Page : 106 pages
File Size : 41,44 MB
Release : 1998-01-01
Category : Science
ISBN : 9781611970005

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Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

Author : Robert Schoen
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 47,67 MB
Release : 2007-05-05
Category : Social Science
ISBN : 1402052308

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Dynamic Population Models is the first book to comprehensively discuss and synthesize the emerging field of dynamic modeling. Incorporating the latest research, it includes thorough discussions of population growth and momentum under gradual fertility declines, the impact of changes in the timing of events on fertility measures, and the complex relationship between period and cohort measures. The book is designed to be accessible to those with only a minimal knowledge of calculus.

Author : Saber Elaydi
Publisher : Springer Nature
Page : 534 pages
File Size : 32,84 MB
Release : 2023-03-25
Category : Mathematics
ISBN : 303125225X

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​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021. The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines. The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Author : Ei Teramoto
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 50,28 MB
Release : 2013-03-08
Category : Mathematics
ISBN : 3642933602

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This volume represents the edited proceedings of the International Symposium on Mathematical Biology held in Kyoto, November 10-15, 1985. The symposium was or ganized by an international committee whose members are: E. Teramoto, M. Yamaguti, S. Amari, S.A. Levin, H. Matsuda, A. Okubo, L.M. Ricciardi, R. Rosen, and L.A. Segel. The symposium included technical sessions with a total of 11 invited papers, 49 contributed papers and a poster session where 40 papers were displayed. These Proceedings consist of selected papers from this symposium. This symposium was the second Kyoto meeting on mathematical topics in biology. The first was held in conjunction with the Sixth International Biophysics Congress in 1978. Since then this field of science has grown enormously, and the number of scientists in the field has rapidly increased. This is also the case in Japan. About 80 young japanese scientists and graduate students participated this time. . The sessions were divided into 4 ; , categories: 1) Mathematical Ecology and Population Biology, 2) Mathematical Theory of Developmental Biology and Morphogenesis, 3) Theoretical Neurosciences, and 4) Cell Kinetics and Other Topics. In every session, there were stimulating and active discussions among the participants. We are convinced that the symposium was highly successful in transmitting scientific information across disciplines and in establishing fruitful contacts among the participants. We owe this success to the cooperation of all participants.

Author : Liviu C. Florescu
Publisher : Walter de Gruyter
Page : 352 pages
File Size : 23,28 MB
Release : 2012-05-29
Category : Mathematics
ISBN : 3110280515

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In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such a relaxation by means of Young measures. This monograph is a self-contained book which gathers all theoretical aspects related to the defining of Young measures (measurability, disintegration, stable convergence, compactness), a book which is also a useful tool for those interested in theoretical foundations of the measure theory. It provides a complete set of classical and recent compactness results in measure and function spaces. The book is organized in three chapters: The first chapter covers background material on measure theory in abstract frame. In the second chapter the measure theory on topological spaces is presented. Compactness results from the first two chapters are used to study Young measures in the third chapter. All results are accompanied by full demonstrations and for many of these results different proofs are given. All statements are fully justified and proved.

Author : Mimmo Iannelli
Publisher : Springer
Page : 357 pages
File Size : 15,54 MB
Release : 2017-08-27
Category : Mathematics
ISBN : 9402411461

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This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.