Observational noise in skew product systems

Physica D: Nonlinear Phenomena

Volumn 107, Issue 1, 1997, Pages 43-56

  Campbell, K M ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Noise; Skew product systems; Synchronisation

Indexed keywords

EID: 0003051765     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00056-0     Document Type: Article

References (26)

1. L. Arnold, Random dynamical systems, Lecture Notes in Math. 1609 (1995) 1-43.
2. P. Ashwin, J. Buescu and I. Stewart, Bubbling of attractors and synchronization of chaotic oscillators, Phys. Lett. A 193 (2) (1994) 126-139.
3. P. Ashwin, J. Buescu and I. Stewart, From attractor to chaotic saddle: A tale of transverse instability, Nonlinearity 9 (3) (1996) 703-737.
4. I.U. Bronshtein, Necessary conditions for the conservation of smooth invariant submanifolds, Differential Equations 22 (4) (1986) 418-424.
5. R. Brown, N.F. Rulkov and N.B. Tufillaro, The effects of additive noise and drift in the dynamics of the driving on chaotic synchronization, Phys. Lett. A 196 (1994) 201-205.
6. R. Brown, N.F. Rulkov and N.B. Tufillaro, Synchronization of chaotic systems: the effects of additive noise and drift in the dynamics of the driving, Phys. Rev. E 50 (6) (1994) 4488-4508.
7. K.M. Campbell, Stability of inertial functions in skew product systems, preprint, University College London (1995).
8. K.M. Campbell and M.E. Davies, The existence of inertial functions in skew product systems, Nonlinearity 9 (1996) 801-817.
9. K.M. Cuomo and A.V. Oppenheim, Circuit implementation of synchronized chaos with applications to cummunications, Phys. Rev. Lett. 71 (1) (1993) 65-68.
10. M.W. Hirsch, C.C. Pugh and M. Shub, Invariant Manifolds, SLN, Vol. 583 (Springer, Berlin, 1977).
11. M. Itoh and H. Murakami, New communication-systems via chaotic synchronizations and modulations, IEICE Trans. Funds. Elec. Comm. Comput. Sci. E 78A (3) (1995) 285-290.
12. L. Kocarev and U. Parlitz, General approach for chaotic synchronization with applications to communication, Phys. Rev. Lett. 74 (25) (1995) 5028-5031.
13. L.M. Kocarev and T.D. Stojanovski, On chaotic synchronization and secure communications, IEICE Trans. Funds. Elec. Comm. Comput. Sci. E 78A (9) (1995) 1142-1147.
14. F. Ledrappier and L.-S. Young, Stability of Lyapunov exponents, Ergodic Theory Dynamical Systems 11 (1991) 469-484.
15. R. Mañé, Persistent manifolds are normally hyperbolic, Bull. AMS 80 (1974) 90-91.
16. R. Mañé, Persistent manifolds are normally hyperbolic, Trans. AMS 246 (1978) 261-283.
17. L.M. Pecora and T.L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (8) (1990) 821-824.
18. L.M. Pecora and T.L. Carroll, Driving systems with chaotic signals, Phys. Rev. A 44 (4) (1991) 2374-2383.
19. L.M. Pecora and T.L. Carroll, Cascading synchronized chaotic systems, Physica D 67 (1993) 126-140.
20. J.H. Peng, E.J. Ding, M. Ding and W. Yang, Synchronizing hyperchaos with a scalar transmitted signal, Phys. Rev. Lett. 76 (6) (1996) 904-907.
21. N. Platt, E.A. Spiegel and C. Tresser, On-off intermittancy: A mechanism for bursting, Phys. Rev. Lett. 70 (3) (1993) 279-282.
22. M. Pollicott, Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds, LMS, Vol. 180 (Cambridge University Press, Cambridge, 1993).
23. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring and H.D.I. Abarbanel, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E (2) (1995) 980-994.
24. N.F. Rulkov, A.R. Volkovskii, A. Rodriguezlozano, E. Delrio and M.G. Velarde, Synchronous chaotic behavior of a response oscillator with chaotic driving, Chaos Solitons and Fractals 4 (2) (1994) 201-211.
25. A. Sato and T. Endo, Experiments of secure communications via chaotic synchronization of phase-locked loops, IEICE Trans. Funds. Elec. Comm. Comput. Sci. E 78A (10) (1995) 1286-1290.
26. M. Shub, Global Stability of Dynamical Systems (Translation of Stabilité Globale Des Systémes Dynamique) (Springer, New York, 1987).