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Author: Dimitri Breda Publisher: Springer ISBN: 149392107X Category : Science Languages : en Pages : 162
Book Description
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.
Author: Dimitri Breda Publisher: Springer ISBN: 149392107X Category : Science Languages : en Pages : 162
Book Description
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.
Author: K. Gopalsamy Publisher: Springer Science & Business Media ISBN: 9780792315940 Category : Mathematics Languages : en Pages : 526
Book Description
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.
Author: R. D. Driver Publisher: Springer Science & Business Media ISBN: 1468494678 Category : Mathematics Languages : en Pages : 513
Book Description
This textbook is designed for the intermediate-level course on ordinary differential equations offered at many universities and colleges. It treats, as standard topics of such a course: existence and uniqueness theory, linear s- terns, stability theory, and introductory phase-plane analysis of autonomous second order systems. The unique feature of the book is its further inc- sion of a substantial introduction to delay differential eq- tions. Such equations are motivated by problems in control theory, physics, biology, ecology, economics, inventory c- trol, and the theory of nuclear reactors. The surge of interest in delay differential equations during the past two or three decades is evidenced by th- sands of research papers on the subject and about 20 published books devoted in whole or in part to these equations. The v * ... books include those of Myskis [1951], El' sgol' c [1955] and [1964], Pinney [1958], Krasovskil [1959], Bellman and Cooke [1963], Norkin [1965], Halanay [1966], Oguztoreli [1966], Lakshmikantham and Leela [1969], Mitropol'skir and Martynjuk [1969], Martynjuk [1971], and Hale [1971], plus a number of symposium and seminar proceedings published in the U.S. and the U.S.S.R. These books have influenced the present textbook.
Author: Alfredo Bellen Publisher: Numerical Mathematics and Scie ISBN: 0199671370 Category : Business & Economics Languages : en Pages : 411
Book Description
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.
Author: Abraham Berman Publisher: Academic Press ISBN: 1483260860 Category : Mathematics Languages : en Pages : 337
Book Description
Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
Author: Balakumar Balachandran Publisher: Springer Science & Business Media ISBN: 0387855955 Category : Technology & Engineering Languages : en Pages : 349
Book Description
Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs). Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory. Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.
Author: hal smith Publisher: Springer Science & Business Media ISBN: 1441976469 Category : Mathematics Languages : en Pages : 178
Book Description
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.
Author: Marc R Roussel Publisher: Morgan & Claypool Publishers ISBN: 1643274643 Category : Science Languages : en Pages : 190
Book Description
This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.
Author: Ravi P. Agarwal Publisher: Springer Science & Business Media ISBN: 1461434556 Category : Mathematics Languages : en Pages : 526
Book Description
This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material. Nonoscillation Theory of Functional Differential Equations with Applications is addressed to a wide audience of researchers in mathematics and practitioners.
Author: Dimitri Breda
Author: Dimitri Breda
Author: K. Gopalsamy
Author: R. D. Driver
Author: Alfredo Bellen
Author: Abraham Berman
Author: Mouffak Benchohra
Author: Balakumar Balachandran
Author: hal smith
Author: Marc R Roussel
Author: Ravi P. Agarwal