Generic Hopf bifurcation from lines of equilibria without parameters: III. Binary oscillations

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 7, 2000, Pages 1613-1621

  Fiedler, Bernold ^a   Liebscher, Stefan ^a   Alexander, J C ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034216035     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400001018     Document Type: Article

References (11)

1. Alexander, J. C. & Auchmuty G. [1986] "Global bifurcation of phase-locked oscillators," Arch. Rat. Mech. Anal. 93, 253-270.
2. Alexander, J. C. & Fiedler, B. [1989] "Global decoupling of coupled symmetric oscillators," Differential Equations, eds. Dafermos, C. M., Ladas, G. C. & Papanicolaou, Lecture Notes in Pure Applied Mathematics 118 (Marcel Dekker Inc, NY).
3. Alexander, J. C. & Fiedler, B. [2000] "Stable and unstable decoupling in squares of additively coupled oscillators," in preparation.
4. Fenichel, N. [1977] "Asymptotic stability with rate conditions. II," Indiana Univ. Math. J. 26, 81-93.
5. Fiedler, B. & Liebscher, S. [2000] "Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws," SIAM J. Math. Anal., to appear.
6. Fiedler, B., Liebscher, S. & Alexander, J. C. [2000] "Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory," J. Diff. Eqs., to appear.
7. Hirsch, M. W., Pugh, C. C. & Shub, M. [1977] Invariant Manifolds, Lecture Notes in Mathematics 583 (Springer-Verlag, Berlin).
8. Levermore, C. D. & Liu, J.-G. [1996] "Large oscillations arising in a dispersive numerical scheme," Physica D99, 191-216.
9. Shoshitaishvili, A. N. [1975] "Bifurcations of topological type of a vector field near a singular point," Tr. Sem. Petrovskogo 1, 279-309.
10. Shub, M. [1987] Global Stability of Dynamical Systems (Springer-Verlag, NY).
11. Wiggins, S. [1994] Normally Hyperbolic Invariant Manifolds in Dynamical Systems (Springer-Verlag, NY).