Nonlinear Differential Equations And Dynamical Systems

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 3642971490
Total Pages : 287 pages
Book Rating : 4.95/5 ( download)

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Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Author : Feliz Manuel Minhós
Publisher : MDPI
ISBN 13 : 3036507108
Total Pages : 158 pages
Book Rating : 4.01/5 ( download)

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Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós and published by MDPI. This book was released on 2021-04-15 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Author : Lawrence Perko
Publisher : Springer Science & Business Media
ISBN 13 : 1468402498
Total Pages : 530 pages
Book Rating : 4.90/5 ( download)

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Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 3642614531
Total Pages : 306 pages
Book Rating : 4.38/5 ( download)

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Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : LUIS MANUEL. BRAGA DA COSTA CAMPOS
Publisher :
ISBN 13 : 9781032653723
Total Pages : 0 pages
Book Rating : 4.28/5 ( download)

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Download or read book Non-Linear Differential Equations and Dynamical Systems written by LUIS MANUEL. BRAGA DA COSTA CAMPOS and published by . This book was released on 2024-06-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This the second book of Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-Volume Set, in the Mathematics and Physics for Science and Technology series. This book considers general first-order differential equations, including non-linear and with variable coefficients.

Author : James D. Meiss
Publisher : SIAM
ISBN 13 : 161197464X
Total Pages : 392 pages
Book Rating : 4.45/5 ( download)

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Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Author : Guido Schneider
Publisher : American Mathematical Soc.
ISBN 13 : 1470436132
Total Pages : 575 pages
Book Rating : 4.31/5 ( download)

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Download or read book Nonlinear PDEs: A Dynamical Systems Approach written by Guido Schneider and published by American Mathematical Soc.. This book was released on 2017-10-26 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

Author : Stephen L. Campbell
Publisher : Princeton University Press
ISBN 13 : 1400841321
Total Pages : 445 pages
Book Rating : 4.25/5 ( download)

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Download or read book Introduction to Differential Equations with Dynamical Systems written by Stephen L. Campbell and published by Princeton University Press. This book was released on 2011-10-14 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Victor A. Galaktionov
Publisher : Springer Science & Business Media
ISBN 13 : 1461220505
Total Pages : 388 pages
Book Rating : 4.03/5 ( download)

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Download or read book A Stability Technique for Evolution Partial Differential Equations written by Victor A. Galaktionov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

Author : Gerald Teschl
Publisher : American Mathematical Society
ISBN 13 : 147047641X
Total Pages : 370 pages
Book Rating : 4.10/5 ( download)

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Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Society. This book was released on 2024-01-12 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Poincaré–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.