Jim M. Cushing - Böcker

This monograph summarizes several decades of collaborations between ecologists and mathematicians, presenting novel applications in biological modeling.

This monograph summarizes several decades of collaborations between ecologists and mathematicians, presenting novel applications in biological modeling.

This text lays the foundation for understanding the beauty and power of discrete-time models. It covers rich mathematical modeling landscapes, each offering deep insights into the dynamics of biological systems. A harmonious balance is achieved between theoretical principles, mathematical rigor, and practical applications. Illustrative examples, numerical simulations, and empirical case studies are provided to enhance mastery of the subject and facilitate the translation of discrete-time mathematical biology into real-world challenges. Mainly geared to upper undergraduates, the text may also be used in graduate courses focusing on discrete-time modeling.  Chapters 1–4 constitute the core of the text. Instructors will find the dependence chart quite useful when designing their particular course. This invaluable resource begins with an exploration of single-species models where frameworks for discrete-time modeling are established. Competition models and Predator-prey interactions are examined next followed by evolutionary models, structured population models, and models of infectious diseases. The consequences of periodic variations, seasonal changes, and cyclic environmental factors on population dynamics and ecological interactions are investigated within the realm of periodically forced biological models.This indispensable resource is structured to support educational settings:A first course in biomathematics, introducing students to the fundamental mathematical techniques essential for biological research.A modeling course with a concentration on developing and analyzing mathematical models that encapsulate biological phenomena.An advanced mathematical biology course that offers an in-depth exploration of complex models and sophisticated mathematical frameworks designed to tackle advanced problems in biology.With its clear exposition and methodical approach, this text educates and inspires students and professionals to apply mathematical biology to real-world situations.  While minimal knowledge of calculus is required, the reader should have a solid mathematical background in linear algebra.

This text lays the foundation for understanding the beauty and power of discrete-time models. It covers rich mathematical modeling landscapes, each offering deep insights into the dynamics of biological systems. A harmonious balance is achieved between theoretical principles, mathematical rigor, and practical applications. Illustrative examples, numerical simulations, and empirical case studies are provided to enhance mastery of the subject and facilitate the translation of discrete-time mathematical biology into real-world challenges. Mainly geared to upper undergraduates, the text may also be used in graduate courses focusing on discrete-time modeling.  Chapters 1–4 constitute the core of the text. Instructors will find the dependence chart quite useful when designing their particular course. This invaluable resource begins with an exploration of single-species models where frameworks for discrete-time modeling are established. Competition models and Predator-prey interactions are examined next followed by evolutionary models, structured population models, and models of infectious diseases. The consequences of periodic variations, seasonal changes, and cyclic environmental factors on population dynamics and ecological interactions are investigated within the realm of periodically forced biological models.This indispensable resource is structured to support educational settings:A first course in biomathematics, introducing students to the fundamental mathematical techniques essential for biological research.A modeling course with a concentration on developing and analyzing mathematical models that encapsulate biological phenomena.An advanced mathematical biology course that offers an in-depth exploration of complex models and sophisticated mathematical frameworks designed to tackle advanced problems in biology.With its clear exposition and methodical approach, this text educates and inspires students and professionals to apply mathematical biology to real-world situations.  While minimal knowledge of calculus is required, the reader should have a solid mathematical background in linear algebra.

This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems.The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology.  It includes four invited papers and eight contributed papers.Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space.This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications.

This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems.The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology.  It includes four invited papers and eight contributed papers.Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space.This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications.

These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems.

These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems.

The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos.All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and engineers with a platform that encouraged them to exchange their innovative ideas in mathematical analysis and its applications as well as to form interdisciplinary collaborations.The content of the book is divided into three parts: Part I contains contributions from participants whose topics are related to nonlinear dynamics and its applications in biological sciences. Part II has contributions which concern topics on nonlinear analysis and its applications to a variety of problems in science, engineering and industry. Part III consists of contributions dealing with some problems in applied analysis.

The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos.All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and engineers with a platform that encouraged them to exchange their innovative ideas in mathematical analysis and its applications as well as to form interdisciplinary collaborations.The content of the book is divided into three parts: Part I contains contributions from participants whose topics are related to nonlinear dynamics and its applications in biological sciences. Part II has contributions which concern topics on nonlinear analysis and its applications to a variety of problems in science, engineering and industry. Part III consists of contributions dealing with some problems in applied analysis.