Methods of Bifurcation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Bifurcation Theory write by S.-N. Chow. This book was released on 2012-12-06. Methods of Bifurcation Theory available in PDF, EPUB and Kindle. An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.
Theory of Functional Differential Equations
Theory of Functional Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory of Functional Differential Equations write by Jack K. Hale. This book was released on 2012-12-06. Theory of Functional Differential Equations available in PDF, EPUB and Kindle. Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred. As a consequence, it was decided not to make a few corrections and additions for a second edition of those notes, but to present a more compre hensive theory. The present work attempts to consolidate those elements of the theory which have stabilized and also to include recent directions of research. The following chapters were not discussed in my original notes. Chapter 1 is an elementary presentation of linear differential difference equations with constant coefficients of retarded and neutral type. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 is devoted entirely to neutral equations. Chapter 13 gives an introduction to the global and generic theory. There is also an appendix on the location of the zeros of characteristic polynomials. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.
Bifurcation Theory of Functional Differential Equations
Bifurcation Theory of Functional Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bifurcation Theory of Functional Differential Equations write by Shangjiang Guo. This book was released on 2013-07-30. Bifurcation Theory of Functional Differential Equations available in PDF, EPUB and Kindle. This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).
Analytic Theory of Global Bifurcation
Analytic Theory of Global Bifurcation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic Theory of Global Bifurcation write by Boris Buffoni. This book was released on 2003-02-02. Analytic Theory of Global Bifurcation available in PDF, EPUB and Kindle. Publisher Description
Elements of Applied Bifurcation Theory
Elements of Applied Bifurcation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of Applied Bifurcation Theory write by Yuri Kuznetsov. This book was released on 2013-03-09. Elements of Applied Bifurcation Theory available in PDF, EPUB and Kindle. Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
