Periodic Solutions Of First Order Functional Differential Equations In Population Dynamics
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| Author | : Seshadev Padhi |
| Publisher | : Springer |
| Total Pages | : 155 |
| Release | : 2014-05-09 |
| Genre | : Mathematics |
| ISBN | : 8132218957 |
This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, and the environment.
| Author | : Frank T. Smith |
| Publisher | : Springer |
| Total Pages | : 703 |
| Release | : 2019-03-14 |
| Genre | : Technology & Engineering |
| ISBN | : 3030122328 |
This book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial. Each chapter enhances our understanding of the research problems in a particular an area of study and highlights the latest advances made in that area. The self-contained contributions make the results and problems discussed accessible to readers, and provides references to enable those interested to follow subsequent studies in still developing fields. Presenting real-world applications, the book is a valuable resource for graduate students, researchers and educators. It appeals to general readers curious about the practical applications of mathematics in diverse scientific areas and social problems.
| Author | : Hemen Dutta |
| Publisher | : CRC Press |
| Total Pages | : 309 |
| Release | : 2020-01-03 |
| Genre | : Mathematics |
| ISBN | : 1000764796 |
Recognized as a "Recommended" title by Choice for their October 2020 issue. Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing. This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences. Presents theory, methods, and applications in a balanced manner Includes the basic developments with full details Contains the most recent advances and offers enough references for further study Written in a self-contained style and provides proof of necessary results Offers research problems to help early career researchers prepare research proposals Mathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.
| Author | : Svetlin G. Georgiev |
| Publisher | : Springer |
| Total Pages | : 886 |
| Release | : 2019-05-03 |
| Genre | : Mathematics |
| ISBN | : 3030154203 |
This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.
| Author | : Anna Capietto |
| Publisher | : Springer |
| Total Pages | : 314 |
| Release | : 2012-12-14 |
| Genre | : Mathematics |
| ISBN | : 3642329063 |
This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.
| Author | : V. Lakshmikantham |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 390 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 146152606X |
Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research. It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems. It is the first book that: (i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay; (ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them; (iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and (iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions. This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.
| Author | : N Perestyuk |
| Publisher | : World Scientific |
| Total Pages | : 474 |
| Release | : 1995-08-31 |
| Genre | : Science |
| ISBN | : 981449982X |
Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts
| Author | : C. De Coster |
| Publisher | : Elsevier |
| Total Pages | : 502 |
| Release | : 2006-03-21 |
| Genre | : Mathematics |
| ISBN | : 0080462472 |
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
| Author | : Stavros Busenberg |
| Publisher | : Elsevier |
| Total Pages | : 376 |
| Release | : 2012-12-02 |
| Genre | : Science |
| ISBN | : 0323153429 |
Differential Equations and Applications in Ecology, Epidemics, and Population Problems is composed of papers and abstracts presented at the 1981 research conference on Differential Equations and Applications to Ecology, Epidemics, and Population Problems held at Harvey Mudd College. The reported researches consist of mathematics that is either a direct outgrowth from questions in population biology and biomathematics, or applicable to such questions. The content of this volume are collected in four groups. The first group addresses aspects of population dynamics that involve the interaction between spatial and temporal effects. The second group covers other questions in population dynamics and some other areas of biomathematics. The third group deals with topics in differential and functional differential equations that are continuing to find important applications in mathematical biology. The last group comprises of work on various aspects of differential equations and dynamical systems, not essentially motivated by biological applications. This book is valuable to students and researchers in theoretical biology and biomathematics, as well as to those interested in modern applications of differential equations.
| Author | : C. M. Dafermos |
| Publisher | : CRC Press |
| Total Pages | : 808 |
| Release | : 2020-08-26 |
| Genre | : Mathematics |
| ISBN | : 100010415X |
This volume is an outcome of the EQUADIFF 87 conference in Greece. It addresses a wide spectrum of topics in the theory and applications of differential equations, ordinary, partial, and functional. The book is intended for mathematics and scientists.
