000 03735nam a22005175i 4500
001 978-1-4419-1740-9
003 DE-He213
005 20140220084507.0
007 cr nn 008mamaa
008 100301s2010 xxu| s |||| 0|eng d
020 _a9781441917409
_9978-1-4419-1740-9
024 7 _a10.1007/978-1-4419-1740-9
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aSeydel, Rüdiger.
_eauthor.
245 1 0 _aPractical Bifurcation and Stability Analysis
_h[electronic resource] /
_cby Rüdiger Seydel.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _aXV, 477p. 200 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInterdisciplinary Applied Mathematics,
_x0939-6047 ;
_v5
505 0 _aand Prerequisites -- Basic Nonlinear Phenomena -- Applications and Extensions -- Principles of Continuation -- Calculation of the Branching Behavior of Nonlinear Equations -- Calculating Branching Behavior of Boundary-Value Problems -- Stability of Periodic Solutions -- Qualitative Instruments -- Chaos.
520 _aThis book covers the central role that bifurcations play in nonlinear phenomena, explaining mechanisms of how stability is gained or lost. It emphasizes practical and computational methods for analyzing dynamical systems. A wide range of phenomena between equilibrium and chaos is explained and illustrated by examples from science and engineering. The book is a practical guide for performing parameter studies and includes exercises. Combining an introduction on the textbook level with an exposition of computational methods, this book addresses the mathematical needs of scientists and engineers. It should be of interest to those in a wide variety of disciplines, including physics, mechanical engineering, electrical engineering, chemistry and chemical engineering, biology, and medicine. Both graduate students (in courses on dynamical systems, stability analysis, differential equations, and chaos) and professionals will be able to use the book equally well. The introduction avoids mathematical formalism, and the only required background is calculus. In the third edition there is a chapter on applications and extensions of standard ODE approaches, for example, to delay equations, to differential-algebraic equations, and to reaction-diffusion problems. Additional material is inserted, including the topics deterministic risk, pattern formation, and control of chaos, and many further references. Review of Earlier Edition: "The outcome is impressive. The book is beautifully written in a style that seeks not only to develop the subject matter but also to expose the thought processes behind the mathematics." Proceedings of the Edinburgh Mathematical Society
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aNumerical analysis.
650 0 _aMathematical physics.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aNumerical Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441917393
830 0 _aInterdisciplinary Applied Mathematics,
_x0939-6047 ;
_v5
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-1740-9
912 _aZDB-2-SMA
999 _c110459
_d110459