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Bifurcation equations of continuous piecewise-linear vector fields

  • Motomasa Komuro
Article

Abstract

This paper provides global equations for certain bifurcation sets of continuous piecewise-linear vector fields. Homoclinic and heteroclinic bifurcations for singular points, and saddle-node, period-doubling and Hopf bifurcations for periodic orbits are studied. The equations are numerically solved to describe the structure of bifurcation sets.

Key words

bifurcation piecewise-linear vector fields 

References

  1. [1]
    L.O. Chua, M. Komuro and T. Matsumoto, The double scroll family. Part I and Part II. IEEE Trans. Circuits and Systems,33 (1986), 1073–1118.Google Scholar
  2. [2]
    P. Gaspard, R. Kapral and G. Nicolis, Bifurcation phenomena near homoclinic systems. J. Statist. Phys.,35 (1984), 697–727.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Glendinings and C. Sparrow, Local and global behavior near homoclinic orbits. J. Statist. Phys.,35 (1984), 645–696.CrossRefMathSciNetGoogle Scholar
  4. [4]
    M. Komuro, Normal forms of continuous piecewise linear vector fields and chaotic attractors. Part I. Japan J. Appl. Math.,5 (1988), 257–304.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    M. Komuro, Normal forms of continuous piecewise linear vector fields and chaotic attractors. Part II. Japan J. Appl. Math.,5 (1988), 503–549.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    T. Poston and I. Stewart, Catastrophe Theory and Its Applications. Pitman Pablishing Limited, London, San Francisco, Melbourne, 1978.MATHGoogle Scholar
  7. [7]
    C. Kahlert and L.O. Chua, A Generalized Canonical Piecewise-Linear Representation. IEEE Trans. Circuits and Systems, CAS-37 (1990), 373–383.MATHMathSciNetGoogle Scholar

Copyright information

© JJIAM Publishing Committee 1992

Authors and Affiliations

  • Motomasa Komuro
    • 1
  1. 1.Department of MathematicsThe Nishi-Tokyo UniversityKitatsurugun, Yamanashi-Pref.Japan

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