Fundamental Concepts in Bifurcations

Takashi Matsumoto, Motomasa Komuro, Hiroshi Kokubu and Ryuji Tokunaga
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Takashi Matsumoto: Waseda University, Department of Electrical Engineering
Motomasa Komuro: The Nishi-Tokyo University, Department of Mathematics
Hiroshi Kokubu: Kyoto University, Department of Mathematics
Ryuji Tokunaga: University of Tsukuba, Institute of Information Science and Electronics

Chapter 3 in Bifurcations, 1993, pp 297-443 from Springer

Abstract: Abstract The objective of this chapter is to give some fundamental notions and results in the theory of dynamical systems as well as their bifurcations, which are important in the qualitative study of dynamical systems and are used in the other two chapters, so that readers can become familiar with those important underlying ideas without referring to other textbooks or articles. Since the other chapters mainly deal with vector fields, that is, continuous dynamical systems, the description of this chapter also places more emphasis on continuous dynamical systems than on discrete dynamical systems, although one section is devoted to these discrete systems.

Keywords: Vector Field; Periodic Orbit; Equilibrium Point; Homoclinic Orbit; Center Manifold (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68243-1_3

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DOI: 10.1007/978-4-431-68243-1_3

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