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Bifurcations pp 297-443 | Cite as

Fundamental Concepts in Bifurcations

  • Takashi Matsumoto
  • Motomasa Komuro
  • Hiroshi Kokubu
  • Ryuji Tokunaga

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Tokyo 1993

Authors and Affiliations

  • Takashi Matsumoto
    • 1
  • Motomasa Komuro
    • 2
  • Hiroshi Kokubu
    • 3
  • Ryuji Tokunaga
    • 4
  1. 1.Department of Electrical EngineeringWaseda UniversityShinjuku-ku, TokyoJapan
  2. 2.Department of MathematicsThe Nishi-Tokyo UniversityUenohara-machi, Kitatsurugun, Yamanashi-PrefectureJapan
  3. 3.Department of MathematicsKyoto UniversityKyotoJapan
  4. 4.Institute of Information Science and ElectronicsUniversity of TsukubaTsukuba Science CityJapan

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