Boundary crisis in quasiperiodically forced systems

Physica D: Nonlinear Phenomena

Volumn 141, Issue 1-2, 2000, Pages 54-64

  Osinga, Hinke M ^a,c   Feudel, Ulrike ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF POTSDAM   (Germany)

^c UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Boundary crisis; Double crisis vertex; Homoclinic tangency

Indexed keywords

EID: 0346479835     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00031-2     Document Type: Article

References (25)

1. C. Grebogi, E. Ott, J.A. Yorke, Crises, sudden changes in chaotic attractors, and transient chaos, Physica D 7 (1983) 181-200.
2. C. Grebogi, E. Ott, F. Romeiras, J.A. Yorke, Critical exponents for crisis-induced intermittency, Phys. Rev. A 36 (11) (1987) 5365-5380.
3. C. Grebogi, E. Ott, J.A. Yorke, Critical exponent of chaotic transients in nonlinear dynamical systems, Phys. Rev. Lett. 57 (11) (1986) 1284-1287.
4. J.A.C. Gallas, C. Grebogi, J.A. Yorke, Vertices in parameter space: double crises which destroy chaotic attractors, Phys. Rev. Lett. 71 (9) (1993) 1359-1362.
5. H.B. Stewart, Y. Ueda, C. Grebogi, J.A. Yorke, Double crises in two-parameter dynamical systems, Phys. Rev. Lett. 75 (13) (1995) 2478-2481.
6. A. Bondeson, E. Ott, T.M. Antonsen, Quasiperiodically forced damped pendula and Schrödinger equations with quasiperiodic potentials: implications of their equivalence, Phys. Rev. Lett. 55 (1985) 2103-2106.
7. M. Ding, C. Grebogi, E. Ott, Evolution of attractors in quasiperiodically forced systems: from quasi periodic to strange nonchaotic to chaotic, Phys. Rev. A 39 (1989) 2593-2598.
8. U. Feudel, M. Safonova, J. Kurths, V.S. Anishchenko, On the destruction of three-dimensional tori, Int. J. Bifurcation Chaos 6 (1996) 1319-1332.
9. D.-R. He, W.J. Yeh, YH. Kao, Transition from quasiperiodicity to chaos in a Josephson junction analog, Phys. Rev. B 30 (1984) 172-178.
10. G.A. Held, C. Jeffries, Quasiperiodic transitions to chaos of instabilities in an electron-hole plasma excited by AC perturbations at one and at two frequencies, Phys. Rev. Lett. 56 (1986) 1183-1186.
11. W.L. Ditto, M.L. Spano, H.T. Savage, S.N. Rauseo, J. Heagy, E. Ott, Experimental observation of a strange nonchaotic attractor, Phys. Rev. Lett. 65 (1990) 533-536.
12. P.R. Chastell, P.A. Glendinning, J. Stark, Locating bifurcations in quasiperiodically forced systems, Phys. Lett. A 200 (1995) 17-26.
13. A. Prasad, V. Mehra, R. Ramaswamy, Intermittency route to strange nonchaotic attractors, Phys. Rev. Lett. 79 (21) (1997) 4127-4130.
14. A. Witt, U. Feudel, A. Pikovsky, Birth of strange nonchaotic attractors due to interior crisis, Physica D 109 (1997) 180-190.
15. T. Yalcinkaya, Y.-C. Lai, Blowout bifurcation route to strange nonchaotic attractors, Phys. Rev. Lett. 77 (1996) 5039-5042.
16. O. Sosnovtseva, U. Feudel, J. Kurths, A. Pikovsky, Multiband strange nonchaotic attractors in quasiperiodically forced systems, Phys. Lett. A 218 (1996) 255-267.
17. M. Hénon, A two-dimensional mapping with a strange attractor, Commun. Math. Phys. 50 (1976) 69-77.
18. K. Alligood, L. Tedeschini-Lalli, J. Yorke, Metamorphoses: sudden jumps in basin boundaries, Commun. Math. Phys. 141 (1991) 1-8 .
19. C. Grebogi, E. Ott, J.A. Yorke, Metamorphoses of basin boundaries in nonlinear dynamical systems, Phys. Rev. Lett. 56 (10) (1986) 1011-1014.
20. C. Grebogi, E. Ott, J.A. Yorke, Basin boundary metamorphoses: changes in accessible boundary orbits, Physica D 24 (1987) 243-262.
21. B.-S. Park, C. Grebogi, Y-C. Lai, Abrupt dimension changes at basin boundary metamorphoses, Int. J. Bifurcation Chaos 2 (3) (1992) 533-541.
22. P. Collet, J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhauser, London, 1980.
23. M.W. Hirsch, C. Pugh, M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, Vol. 583, Springer, Berlin, 1977.
24. H.W. Broer, H.M. Osinga, G. Vegter, Algorithms for computing normally hyperbolic invariant manifolds, Z. Angew. Math. Phys. 48 (1997) 480-524.
25. B. Krauskopf, H.M. Osinga, Growing ID and quasi 2D unstable manifolds of maps, J. Comput. Phys. 146 (1) (1998) 404-419.