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Titlebook: Elements of Applied Bifurcation Theory; Yuri A. Kuznetsov Book 20043rd edition Springer Science+Business Media New York 2004 Mathematica.a

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发表于 2025-3-21 17:18:37 | 显示全部楼层 |阅读模式
书目名称Elements of Applied Bifurcation Theory
编辑Yuri A. Kuznetsov
视频video
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Elements of Applied Bifurcation Theory;  Yuri A. Kuznetsov Book 20043rd edition Springer Science+Business Media New York 2004 Mathematica.a
描述The years that have passed since the publication of the first edition of this book proved that the basic principles used to select and present the material made sense. The idea was to write a simple text that could serve as a seri­ ous introduction to the subject. Of course, the meaning of "simplicity" varies from person to person and from country to country. The word "introduction" contains even more ambiguity. To start reading this book, only a moder­ ate knowledge of linear algebra and calculus is required. Other preliminaries, qualified as "elementary" in modern mathematics, are explicitly formulated in the book. These include the Fredholm Alternative for linear systems and the multidimensional Implicit Function Theorem. Using these very limited tools, a framewo:k of notions, results, and methods is gradually built that allows one to read (and possibly write) scientific papers on bifurcations of nonlinear dynamical systems. Among other things, progress in the sciences means that mathematical results and methods that once were new become standard and routinely used by the research and development community. Hopefully, this edition of the book will contribute to this process. The
出版日期Book 20043rd edition
关键词Mathematica; applied mathematics; bifurcation; dynamical systems; numerical analysis; numerical method; st
版次3
doihttps://doi.org/10.1007/978-1-4757-3978-7
isbn_ebook978-1-4757-3978-7Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 2004
The information of publication is updating

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Deric St. Julian Bown, F.B.D.S., F.R.S.A.,ions of ., and their .. As we shall see while analyzing the ., invariant sets can have very complex structures. This is closely related to the fact discovered in the 1960s that rather simple dynamical systems may behave “randomly,” or “chaotically.” Finally, we discuss how differential equations can
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https://doi.org/10.1007/978-3-319-44573-1 systems and their classification, bifurcations and bifurcation diagrams, and topological normal forms for bifurcations. The last section is devoted to the more abstract notion of structural stability. In this chapter we will be dealing only with dynamical systems in the state space . = ℝ..
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Irving Fisher and Interest Theory dynamical systems. First we consider in detail two- and three-dimensional cases where geometrical intuition can be fully exploited. Then we show how to reduce generic .-dimensional cases to the considered ones plus a four-dimensional case treated in Appendix A.
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Ben Gidley,Peter Scholten,Ilona van Breugellist of all generic one-parameter bifurcations is unknown. In this chapter we study several unrelated bifurcations that occur in one-parameter continuous-time dynamical systems.where . is a smooth function of (., .). We start by considering global bifurcations of orbits that are homoclinic to nonhyp
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Mainstreaming Islam in Indonesiach bifurcations. Then, we derive a . for each bifurcation in the minimal possible phase dimension and specify relevant genericity conditions. Next, we truncate higher-order terms and present the bifurcation diagrams of the resulting system. The analysis is completed by a discussion of the effect of
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https://doi.org/10.1007/978-981-10-5320-7r the final two bifurcations in the previous chapter, the description of the majority of these bifurcations is incomplete in principle. For all but two cases, only . normal forms can be constructed. Some of these normal forms will be presented in terms of associated planar continuous-time systems wh
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