Averaging Methods In Nonlinear Dynamical Systems
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Author |
: Jan A. Sanders |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 259 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9781475745757 |
ISBN-13 |
: 1475745753 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Averaging Methods in Nonlinear Dynamical Systems by : Jan A. Sanders
In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.
Author |
: Jan A. Sanders |
Publisher |
: |
Total Pages |
: 264 |
Release |
: 2014-01-15 |
ISBN-10 |
: 1475745761 |
ISBN-13 |
: 9781475745764 |
Rating |
: 4/5 (61 Downloads) |
Synopsis Averaging Methods in Nonlinear Dynamical Systems by : Jan A. Sanders
Author |
: Ferdinand Verhulst |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 287 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642971495 |
ISBN-13 |
: 3642971490 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst
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 |
: John Guckenheimer |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 475 |
Release |
: 2013-11-21 |
ISBN-10 |
: 9781461211402 |
ISBN-13 |
: 1461211409 |
Rating |
: 4/5 (02 Downloads) |
Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Author |
: Steven H. Strogatz |
Publisher |
: CRC Press |
Total Pages |
: 532 |
Release |
: 2018-05-04 |
ISBN-10 |
: 9780429961113 |
ISBN-13 |
: 0429961111 |
Rating |
: 4/5 (13 Downloads) |
Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author |
: Françoise Pène |
Publisher |
: |
Total Pages |
: 52 |
Release |
: 2001 |
ISBN-10 |
: OCLC:897808595 |
ISBN-13 |
: |
Rating |
: 4/5 (95 Downloads) |
Synopsis Averaging method for differential equations perturbed by dynamical systems by : Françoise Pène
Author |
: |
Publisher |
: Elsevier |
Total Pages |
: 401 |
Release |
: 2007-04-03 |
ISBN-10 |
: 9780080489469 |
ISBN-13 |
: 008048946X |
Rating |
: 4/5 (69 Downloads) |
Synopsis Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances by :
The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner.· Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context· Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part)· Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)
Author |
: John Guckenheimer |
Publisher |
: |
Total Pages |
: 484 |
Release |
: 2014-09-01 |
ISBN-10 |
: 1461211417 |
ISBN-13 |
: 9781461211419 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer
Author |
: E. Atlee Jackson |
Publisher |
: CUP Archive |
Total Pages |
: 676 |
Release |
: 1989 |
ISBN-10 |
: 0521426332 |
ISBN-13 |
: 9780521426336 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Perspectives of Nonlinear Dynamics: Volume 2 by : E. Atlee Jackson
The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.
Author |
: Dimitri Volchenkov |
Publisher |
: Springer |
Total Pages |
: 316 |
Release |
: 2017-06-24 |
ISBN-10 |
: 9783319580623 |
ISBN-13 |
: 3319580620 |
Rating |
: 4/5 (23 Downloads) |
Synopsis Regularity and Stochasticity of Nonlinear Dynamical Systems by : Dimitri Volchenkov
This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.