On the unfolding of a blowout bifurcation

Physica D: Nonlinear Phenomena

Volumn 111, Issue 1-4, 1998, Pages 81-95

  Ashwin, Peter ^a   Aston, Philip J ^a   Nicol, Matthew ^b  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22244450725     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)80006-1     Document Type: Article

References (26)

1. J.C. Alexander, I. Kan, J.A. Yorke and Zhiping You, Riddled basins, Int. J. Bif. Chaos 2 (1992) 795-813.
2. P. Ashwin, Attractors stuck on to invariant subspaces, Phys. Lett. A 209 (1995) 338-344.
3. P. Ashwin, J. Buescu and I.N. Stewart, Bubbling of attractors and synchronisation of oscillators, Phys. Lett. A 193 (1994) 126-139.
4. P. Ashwin, J. Buescu and I.N. Stewart, From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity 9 (1996) 703-737.
5. P.J. Aston, Bifurcation and chaos in iterated maps with O(2) symmetry, Int. J. Bif. Chaos 5 (1995) 701-724.
6. P.J. Aston and M. Dellnitz, Symmetry breaking bifurcation of chaotic attractors, Int. J. Bif. Chaos 5 (1995) 1643-1676.
7. A. Cenys and H. Lustfeld, Statistical properties of the noisy on-off intermittency, J. Phys. A Math. Gen. 29 (1996) 11-20.
8. G.R. Grimmett and D.R. Stirzaker, Probability and Random Processes (Clarendon Press, Oxford, 1992).
9. P.W. Hammer, N. Platt, S.M. Hammel, J.F. Heagy and B.D. Lee, Experimental observation of on-off intermittency, Phys. Rev. Lett. 73 (1994) 1095-1098.
10. J.F. Heagy, N. Platt and S.M. Hammel, Characterization of on-off intermittency, Phys. Rev. E 49 (1994) 1140-1150.
11. T. Kapitaniak, Transition to hyperchaos in chaotically forced coupled oscillators, Phys. Rev. E 47 (1993) R2975-R2978.
12. Y.-C. Lai, Symmetry-breaking bifurcation with on-off intermittency in chaotic dynamical systems. Phys. Rev. E 53 (1996) R4267-R4270.
13. I. Melbourne, M. Dellnitz and M. Golubitsky, The structure of symmetric attractors, Arch. Rat. Mech. Anal. 123 (1993) 75-98.
14. J. Milnor, On the concept of attractor, Commun. Math. Phys. 99 (1985) 177-195;
15. Comments, Commun. Math. Phys. 102 (1985) 517-519.
16. V.I. Oseledec. A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Trans. Moscow. Math. Soc. 19 (1968) 197-231.
17. E. Ott and J.C. Sommerer, Blowout bifurcations: the occurrence of riddled basins and on-off intermittency, Phys. Lett. A 188 (1994) 39-47.
18. E. Ott, J.C. Sommerer, J.C. Alexander, I. Kan and J.A. Yorke, Scaling behaviour of chaotic systems with riddled basins, Phys. Rev. Lett. 71 (1993) 4134-4137.
19. E. Ott, J.C. Sommerer, J.C. Alexander, I. Kan and J.A. Yorke, A transition to chaotic attractors with riddled basins, Physica D 76 (1994) 384-410.
20. A.S. Pikovsky, On the interaction of strange attractors, Z. Phys. B 55 (1984) 149-154.
21. A.S. Pikovsky and P. Grassberger, Symmetry breaking of coupled chaotic attractors, J. Phys. A 24 (1991) 4587-4597.
22. N. Platt, S.M. Hammel and J.F. Heagy, Effects of additive noise on on-off intermittency, Phys. Rev. Lett. 72 (1994) 3498-3501.
23. N. Platt, E.A. Spiegel and C. Tresser, On-off intermittency; a mechanism for bursting, Phys. Rev. Lett. 70 (1993) 279-282.
24. K. Sigmund, Time averages for unpredictable orbits of deterministic systems, Ann. Oper. Res. 37 (1992) 217-228.
25. M. da Sousa Vieira, A.J. Lichtenberg and M.A. Lieberman, Synchronisation of regular and chaotic systems, Phys. Rev. A 46 (1992) R7359-R7362.
26. T. Yamada and H. Fujisaka, Stability theory of synchronised motion in coupled-oscillator systems, Prog. Theor. Phys. 70 (1984) 1240-1248.