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Some examples of bifurcation

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Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1057)

Keywords

  • Periodic Solution
  • Hopf Bifurcation
  • Subharmonic Solution
  • Piecewise Linear System
  • Characteristic Multiplier

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References

  1. E. Hopf, Abzweigung einer periodischer Lösung von einer stationären Lösung eines Differentialsystems, Ber. Math. Phys. Sachsische Akad. der Wissenschaften, Leipzig 94 (1942), 1–22.

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  2. W. S. Loud, Behavior of the period of solutions of certain plane autonomous systems near centers. Contr. Diff. Eq. 3 (1964), 21–36.

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  3. W. S. Loud, Periodic solutions of second order differential equations of Duffing type. Proc. U.S.-Japan Seminar on Differential and Functional Equations, W. A. Benjamin, Inc. 1967, 199–224.

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  4. W. S. Loud, Branching phenomena for periodic solutions of nonautonomous piecewise linear systems. Int. J. Nonlinear Mechanics 3 (1968), 273–293.

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  5. W. S. Loud, Nonsymmetric periodic solutions of certain second order nonlinear differential equations. J. Diff. Eq. 5 (1969), 352–368.

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  6. W. S. Loud, Subharmonic solutions of second order equations arising near harmonic solutions. J. Diff. Eq. 11 (1972), 628–660.

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  7. W. S. Loud, Subharmonic solutions of second order equations arising near harmonic solutions. J. Diff. Eq. (1984) to appear.

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  8. J. E. Marsden and M. F. McCracken, The Hopf bifurcation and its applications. Springer Verlag, N. Y., 1976.

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  9. H. L. Turrittin and W. J. W. Culmer, A peculiar periodic solution of a modified Duffing's equation. Ann. di Mat. pura ed appl. (IV) 44 (1957), 23–34.

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© 1984 Springer-Verlag

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Loud, W.S. (1984). Some examples of bifurcation. In: Salvadori, L. (eds) Bifurcation Theory and Applications. Lecture Notes in Mathematics, vol 1057. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098597

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  • DOI: https://doi.org/10.1007/BFb0098597

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12931-8

  • Online ISBN: 978-3-540-38812-8

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