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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, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.
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 of interest in the modern as well as the clas sical techniques of applied mathematics.
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. Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references 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.
Differential Equations and Dynamical Systems – Lawrence Perko – Google Books
The text succeeds admiraby The Best Books of Govaerts No preview available – Multiscale Methods Grigoris Pavliotis. Each section closes with a set of problems, many of which are quite interesting and round out the text material 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 xifferential advanced textbooks and research level monographs.
Description This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Introduction to Perturbation Methods Mark H.
Check out the top books of the year on our page Best Books of Although the main topic of the book is the local dofferential global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text.
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Geometric Methods and Applications Jean Gallier. Common terms and phrases analytic system behavior bifurcation diagram bifurcation surface bifurcation value bifurcations that occur center manifold Chapter Cl E codimension compute Corollary defined determined differential equation dynamical system eigenvalues eigenvectors equilibrium point family of periodic family of rotated field f finite number flow given global phase portrait Hamiltonian system homoclinic loop homoclinic orbit Hopf bifurcation hyperbolic initial value problem Lemma Lienard system limit cycles linear system maximal interval Melnikov function neighborhood node nonhyperbolic critical point nonlinear system normal form one-parameter family open subset origin parameter periodic orbit planar systems Poincare map Poincare sphere Poincare-Bendixson Theorem point XQ polynomial PROBLEM SET proof rotated vector fields saddle saddle-node bifurcation satisfies Section 4.
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Differential Equations and Dynamical Systems
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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.
The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics.
Differential Equations and Dynamical Systems. User Review – Flag as inappropriate pls send this book for us. Differential Equations and Dynamical Systems.
This renewal of interest, both in research Back cover copy This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations adn dynamical systems. Other books in this series. Account Options Sign in.
In addition to minor difderential and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise’s algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.
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