Detecting symmetry breaking bifurcations in the system describing the dynamics of coupled arrays of Josephson junctions

Physica D: Nonlinear Phenomena

Volumn 91, Issue 1-2, 1996, Pages 67-85

  Tchistiakov, V ^a  

^a UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Detective; Sn symmetry; Symmetry increasing bifurcation

Indexed keywords

EID: 0040004859     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00253-7     Document Type: Article

References (22)

1. N symmetry, Nonlinearity 4 (1991) 861-902.
2. 2 symmetry, J. Nonlin. Sci. 4 (1994) 195-219.
3. P. Ashwin and I. Melbourne, Symmetry Groups of Attractors, Archive for Rational Mechanics and Analysis 126(1) (1994) 59-78.
4. P. Ashwin, G.P. King and J.W. Swift, Three identical oscillators with symmetric coupling, Nonlinearity 3 (1990) 585-601.
5. P. Ashwin and J.W. Swift, The dynamics of n weakly coupled identical oscillators, J. Nonlin. Sci. (1992) 69-108.
6. E. Barany, M. Dellnitz and M. Golubitsky, Detecting the Symmetry of Attractors, Physica D 67 (1993) 66-87.
7. W. Burnside, Theory of groups of finite order (Dover Publications, Inc., 1955).
8. P. Chossat and M. Golubitsky, Symmetry increasing bifurcations of chaotic attractors, Physica D 32 (1988) 423-436.
9. M. Dellnitz, M. Golubitsky and M. Nicol, Symmetry of attractors and the Karhunen-Loeve decomposition, in: Trends and Perspectives in Applied Mathematics, ed. L. Sirovich, Appl. Math. Sci. 100 (1994) 73-108.
10. E.J. Doedel, AUTO: A program for automatic bifurcation analysis of autonomous systems, Cong. Num. 30 (1981) 265-284.
11. B. Fiedler, Global bifurcation of periodic solutions with symmetry (Springer-Verlag, 1988).
12. M. Field and M. Golubitsky, Symmetry in chaos (Oxford University press, Oxford, 1992).
13. M. Golubitsky and M. Nicol, Symmetry detectives for SBR attractors, preprint (1994).
14. B.D. Josephson, Phys. Lett. 1 (1961) 251.
15. M. Kroon and I. Stewart, Detecting the symmetry of attractors for six oscillators coupled in a ring, preprint (1994).
16. W. Miller, Symmetry Groups and Their Applications (Acad. Press, 1972).
17. S. Nichols and K. Wiesenfeld, Ubiquitous neutral stability of splay-phase states, Phys. Rev. A 45 (1992) 8430.
18. K. Otsuka, Phys. Rev. Lett. 67 (1991) 1090.
19. J. Patera, R.T. Sharp and P. Winternitz, Polynomial irreducible tensors for point groups, J. Math. Phys. 19(11) (1978) 2362-2376.
20. K.Y. Tsang and K. Wiesenfeld, Appl. Phys. Lett. 56 (1990) 495.
21. K.Y. Tsang, R.E. Mirollo, S.H. Strogatz and K. Wiesenfeld, Dynamics of a globally coupled oscillator array, Physica D 48 (1991) 102.
22. K. Wiesenfeld and P. Hadley, Phys. Rev. Lett. 62 (1989) 1338.