Models Of Delay Differential Equations
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An Introduction To Delay Differential Equations With Applications To The Life Sciences
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Author : hal smith
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-29
An Introduction To Delay Differential Equations With Applications To The Life Sciences written by hal smith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-29 with Mathematics categories.
This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the applications quickly. The author has used preliminary notes in teaching such a course at Arizona State University over the past two years. This book focuses on the key tools necessary to understand the applications literature involving delay equations and to construct and analyze mathematical models involving delay differential equations. The book begins with a survey of mathematical models involving delay equations.
Models Of Delay Differential Equations
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Author : Francisco Rodríguez
language : en
Publisher:
Release Date : 2021
Models Of Delay Differential Equations written by Francisco Rodríguez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering.
Delay Differential Equations And Applications To Biology
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Author : Fathalla A. Rihan
language : en
Publisher: Springer Nature
Release Date : 2021-08-19
Delay Differential Equations And Applications To Biology written by Fathalla A. Rihan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-19 with Mathematics categories.
This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.
Delay Differential Equations And Applications
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Author : O. Arino
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-25
Delay Differential Equations And Applications written by O. Arino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-25 with Mathematics categories.
This book groups material that was used for the Marrakech 2002 School on Delay Di'erential Equations and Applications. The school was held from September 9-21 2002 at the Semlalia College of Sciences of the Cadi Ayyad University, Marrakech, Morocco. 47 participants and 15 instructors originating from 21 countries attended the school. Fin- cial limitations only allowed support for part of the people from Africa andAsiawhohadexpressedtheirinterestintheschoolandhadhopedto come. Theschoolwassupportedby'nancementsfromNATO-ASI(Nato advanced School), the International Centre of Pure and Applied Mat- matics (CIMPA, Nice, France) and Cadi Ayyad University. The activity of the school consisted in courses, plenary lectures (3) and communi- tions (9), from Monday through Friday, 8. 30 am to 6. 30 pm. Courses were divided into units of 45mn duration, taught by block of two units, with a short 5mn break between two units within a block, and a 25mn break between two blocks. The school was intended for mathematicians willing to acquire some familiarity with delay di'erential equations or enhance their knowledge on this subject. The aim was indeed to extend the basic set of knowledge, including ordinary di'erential equations and semilinearevolutionequations,suchasforexamplethedi'usion-reaction equations arising in morphogenesis or the Belouzov-Zhabotinsky ch- ical reaction, and the classic approach for the resolution of these eq- tions by perturbation, to equations having in addition terms involving past values of the solution.
Stability Of Linear Delay Differential Equations
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Author : Dimitri Breda
language : en
Publisher: Springer
Release Date : 2014-10-21
Stability Of Linear Delay Differential Equations written by Dimitri Breda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-21 with Science categories.
This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.
Time Delay Ode Pde Models
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Author : W.E. Schiesser
language : en
Publisher: CRC Press
Release Date : 2019-11-25
Time Delay Ode Pde Models written by W.E. Schiesser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-25 with Mathematics categories.
Time delayed (lagged) variables are an inherent feature of biological/physiological systems. For example, infection from a disease may at first be asymptomatic, and only after a delay is the infection apparent so that treatment can begin.Thus, to adequately describe physiological systems, time delays are frequently required and must be included in the equations of mathematical models. The intent of this book is to present a methodology for the formulation and computer implementation of mathematical models based on time delay ordinary differential equations (DODEs) and partial differential equations (DPDEs). The DODE/DPDE methodology is presented through a series of example applications, particularly in biomedical science and engineering (BMSE). The computer-based implementation of the example models is explained with routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The DPDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The example applications can first be executed to confirm the reported solutions, then extended by variation of the parameters and the equation terms, and even the forumulation and use of alternative DODE/DPDE models. • Introduces time delay ordinary and partial differential equations (DODE/DPDEs) and their numerical computer-based integration (solution) • Illustrates the computer implementation of DODE/DPDE models with coding (programming) in R, a quality, open-source scientific programming system readily available from the Internet • Applies DODE/DPDE models to biological/physiological systems through a series of examples • Provides the R routines for all of the illustrative applications through a download link • Facilitates the use of the models with reasonable time and effort on modest computers
Stability And Oscillations In Delay Differential Equations Of Population Dynamics
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Author : K. Gopalsamy
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-03-31
Stability And Oscillations In Delay Differential Equations Of Population Dynamics written by K. Gopalsamy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-31 with Mathematics categories.
This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.
Delay Differential Equations
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Author : Yang Kuang
language : en
Publisher: Academic Press
Release Date : 1993-03-05
Delay Differential Equations written by Yang Kuang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-05 with Mathematics categories.
Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems. The book treats both autonomous and nonautonomous systems with various delays. Key topics addressed are the possible delay influence on the dynamics of the system, such as stability switching as time delay increases, the long time coexistence of populations, and the oscillatory aspects of the dynamics. The book also includes coverage of the interplay of spatial diffusion and time delays in some diffusive delay population models. The treatment presented in this monograph will be of great value in the study of various classes of DDEs and their multidisciplinary applications.
Models Of Delay Differential Equations
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Author : Francisco Rodríguez
language : en
Publisher:
Release Date : 2021-06-30
Models Of Delay Differential Equations written by Francisco Rodríguez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-30 with categories.
This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering
Numerical Methods For Delay Differential Equations
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Author : Alfredo Bellen
language : en
Publisher: Numerical Mathematics and Scie
Release Date : 2013-01-10
Numerical Methods For Delay Differential Equations written by Alfredo Bellen and has been published by Numerical Mathematics and Scie this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-10 with Business & Economics categories.
This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.