Differential Equations and Dynamical Systems

Author: Lawrence Perko
Publisher: Springer Science & Business Media
ISBN: 1461300037
Format: PDF, Docs
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This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.

Differential Equations and Dynamical Systems

Author: Lawrence Perko
Publisher: Springer Science & Business Media
ISBN: 1468403923
Format: PDF, Docs
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Although this systematic study of autonomous systems begins with a thorough treatment of linear systems, the main emphasis is on local and global behavior of nonlinear systems. The main purpose of this revised edition is to introduce students to the qualitative and geometric theory of ordinary differential equations as well as serving as a reference book for mathematicians researching dynamical systems. Readers will find that, except for certain topics of current mathematical research, such as the number of limit cycles and the nature of attracting sets of dynamical systems, the global qualitative theory of a nonlinear dynamical system leads to an understanding of the solution set of the nonlinear system to rival that which we have of linear flows.

Differential Equations and Dynamical Systems

Author: Lawrence Perko
Publisher: Springer Science & Business Media
ISBN: 9780387951164
Format: PDF, Mobi
Download Now
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.

Ordinary Differential Equations and Dynamical Systems

Author: Gerald Teschl
Publisher: American Mathematical Soc.
ISBN: 0821883283
Format: PDF, Mobi
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This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Nonlinear Differential Equations and Dynamical Systems

Author: Ferdinand Verhulst
Publisher: Springer Science & Business Media
ISBN: 3642614531
Format: PDF, Kindle
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For lecture courses that cover the classical theory of nonlinear differential equations associated with Poincare and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos, this text is ideal. Its excellent pedagogical style typically consists of an insightful overview followed by theorems, illustrative examples, and exercises.

Introduction to Differential Equations with Dynamical Systems

Author: Stephen L. Campbell
Publisher: Princeton University Press
ISBN: 1400841321
Format: PDF, Kindle
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Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

Ordinary Differential Equations and Dynamical Systems

Author: Thomas C. Sideris
Publisher: Springer Science & Business Media
ISBN: 9462390215
Format: PDF, Docs
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This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.

Differential Equations A Dynamical Systems Approach

Author: John H. Hubbard
Publisher: Springer Science & Business Media
ISBN: 9780387972862
Format: PDF, ePub
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This corrected third printing retains the authors'main emphasis on ordinary differential equations. It is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. The authors have taken the view that a differential equations theory defines functions; the object of the theory is to understand the behaviour of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.

Differential Equations Dynamical Systems and Linear Algebra

Author: Morris W. Hirsch
Publisher: Academic Press
ISBN: 0080873766
Format: PDF, Mobi
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This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Differential Equations Dynamical Systems and an Introduction to Chaos

Author: Morris W. Hirsch
Publisher: Academic Press
ISBN: 0123497035
Format: PDF, Mobi
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This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It is an update of one of Academic Press's most successful mathematics texts ever published, which has become the standard textbook for graduate courses in this area. The authors are tops in the field of advanced mathematics. Steve Smale is a Field's Medalist, which equates to being a Nobel prize winner in mathematics. Bob Devaney has authored several leading books in this subject area. Linear algebra prerequisites toned down from first edition Inclusion of analysis of examples of chaotic systems, including Lorenz, Rosssler, and Shilnikov systems Bifurcation theory included throughout.