Effect of noise on chaotic scattering

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 79, Issue 4, 2009, Pages

  Seoane, Jesús M ^a   Huang, Liang ^b   Sanjuán, Miguel A F ^a   Lai, Ying Cheng ^b,c  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b Arizona State University   (United States)

^c ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SCATTERING; CONTINUOUS TIME MODELS; DECAY RATE; DISCRETE-TIME; EXPONENTIAL DECAY RATES; NOISE INTENSITIES; NUMERICAL RESULTS; SCATTERING REGIONS; SCATTERING SYSTEMS;

CONTINUOUS TIME SYSTEMS;

SCATTERING;

EID: 66349112875     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.047202     Document Type: Article

References (33)

1. See, for example, the following focus issue: E. Ott and T. Tél, Chaos 3, 417 (1993). 10.1063/1.165949
2. Some representative early papers on chaotic scattering are: C. Jung, J. Phys. A 19, 1345 (1986) 10.1088/0305-4470/19/8/016
3. M. Hénon, Physica D 33, 132 (1988) 10.1016/S0167-2789(98)90015-X
4. P. Gaspard and S. A. Rice, J. Chem. Phys. 90, 2225 (1989) 10.1063/1.456017
5. G. Troll and U. Smilansky, Physica D 35, 34 (1989). 10.1016/0167-2789(89) 90095-X
6. S. Bleher, C. Grebogi, and E. Ott, Physica D 46, 87 (1990). 10.1016/0167-2789(90)90114-5
7. M. Ding, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. A 42, 7025 (1990). 10.1103/PhysRevA.42.7025
8. A. E. Motter and Y. C. Lai, Phys. Rev. E 65, 015205 (R) (2001). 10.1103/PhysRevE.65.015205
9. J. M. Seoane, J. Aguirre, M. A. F. Sanjuán, and Y.-C. Lai, Chaos 16, 023101 (2006). 10.1063/1.2173342
10. J. M. Seoane, M. A. F. Sanjuán, and Y.-C. Lai, Phys. Rev. E 76, 016208 (2007). 10.1103/PhysRevE.76.016208
11. J. Lehmann, P. Reimann, and P. Hänggi, Phys. Rev. Lett. 84, 1639 (2000). 10.1103/PhysRevLett.84.1639
12. P. Mills, Commun. Nonlinear Sci. Numer. Simul. 11, 899 (2006). 10.1016/j.cnsns.2005.02.003
13. J. M. Seoane and M. A. F. Sanjuán, Phys. Lett. A 372, 110 (2008).
14. This has been demonstrated numerically in Ref..
15. Y.-T. Lau, J. M. Finn, and E. Ott, Phys. Rev. Lett. 66, 978 (1991). 10.1103/PhysRevLett.66.978
16. M. Hénon and C. Heiles, Astron. J. 69, 73 (1964). 10.1086/109234
17. J. Aguirre, J. C. Vallejo, and M. A. F. Sanjuán, Phys. Rev. E 64, 066208 (2001). 10.1103/PhysRevE.64.066208
18. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, New York, 1999).
19. J. Kennedy and J. A. Yorke, Physica D 51, 213 (1991) 10.1016/0167- 2789(91)90234-Z
20. Z. Toroczkai, G. Károlyi, A. Péntek, T. Tél, C. Grebogi, and J. A. Yorke, Physica A 239, 235 (1997) 10.1016/S0378-4371(96)00482- 7
21. M. A. F. Sanjuán, J. Kennedy, C. Grebogi, and J. A. Yorke, Chaos 7, 125 (1997) 10.1063/1.166244
22. J. Kennedy, M. A. F. Sanjuán, J. A. Yorke, and C. Grebogi, Topology and Its Applications 94, 207 (1999) 10.1016/S0166-8641(98)00032-7
23. H. E. Nusse and J. A. Yorke, Science 271, 1376 (1996) 10.1126/science.271.5254.1376
24. H. E. Nusse and J. A. Yorke, Physica D 90, 242 (1996) 10.1016/0167-2789(95)00249-9
25. H. E. Nusse and J. A. Yorke, Phys. Rev. Lett. 84, 626 (2000) 10.1103/PhysRevLett.84.626
26. J. Aguirre and M. A. F. Sanjuán, Physica D 171, 41 (2002). 10.1016/S0167-2789(02)00565-1
27. J. A. Almendral and M. A. F. Sanjuán, J. Phys. A 36, 695 (2003). 10.1088/0305-4470/36/3/308
28. C. F. F. Karney, Physica D 8, 360 (1983) 10.1016/0167-2789(83)90232-4
29. B. V. Chirikov and D. L. Shepelyansky, Physica D 13, 395 (1984) 10.1016/0167-2789(84)90140-4
30. J. Meiss and E. Ott, Physica D 20, 387 (1986) 10.1016/0167-2789(86)90041- 2
31. Y.-C. Lai, M. Ding, C. Grebogi, and R. Blümel, Phys. Rev. A 46, 4661 (1992). 10.1103/PhysRevA.46.4661
32. This has been tested numerically on a damped harmonic oscillator in a noisy environment.
33. Defining T0 =1/γ, we have R (t) ∼ e-T/ T0. The average lifetime of the particles is T = T R (T) dT = T0, which depends on initial energy E. In general, we can write T0 =g (E) or γ=f (E).