Constructive analysis of noise-induced transitions for coexisting periodic attractors of the Lorenz model

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

Volumn 79, Issue 4, 2009, Pages

  Bashkirtseva, Irina ^a   Ryashko, Lev ^a  

^a URAL FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRIC METHODS; LIMIT CYCLES; LORENZ MODELS; NOISE-INDUCED TRANSITIONS; PERIOD-DOUBLING BIFURCATIONS; PERIODIC ATTRACTORS; POINCARE SECTIONS; SENSITIVITY FUNCTIONS; STRUCTURAL STABILIZATIONS; TRANSITION TO CHAOS;

GAUSSIAN NOISE (ELECTRONIC);

EID: 65449179268     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.041106     Document Type: Article

References (39)

1. L. S. Pontryagin, A. A. Andronov, and A. A. Witt, Zh. Eksp. Teor. Fiz. 3, 165 (1933).
2. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963).
3. C. Kurrer and K. Schulten, Physica D 50, 311 (1991). 10.1016/0167- 2789(91)90001-P
4. F. Baras, Lecture Notes in Physics (Springer-Verlag, New York, 1997), Vol. 484, pp. 167-178.
5. L. Arnold, G. Bleckert, and K. Schenk-Hoppe, Stochastic Dynamics (Bremen, 1997) (Springer, New York, 1999), pp. 71-92.
6. V. N. Smelyanskiy, M. I. Dykman, and R. S. Maier, Phys. Rev. E 55, 2369 (1997). 10.1103/PhysRevE.55.2369
7. P. S. Landa and P. V. E. McClintock, Phys. Rep. 323, 1 (2000). 10.1016/S0370-1573(99)00043-5
8. L. Gammaitoni, Rev. Mod. Phys. 70, 223 (1998). 10.1103/RevModPhys.70.223
9. M. D. McDonnell, N. G. Stocks, C. E. M. Pearce, and D. Abbott, Stochastic Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University Press, New York, 2008).
10. W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer, Berlin, 1984).
11. K. Matsumoto and I. Tsuda, J. Stat. Phys. 33, 757 (1983). 10.1007/BF01018842
12. F. Gassmann, Phys. Rev. E 55, 2215 (1997). 10.1103/PhysRevE.55.2215
13. J. B. Gao, S. K. Hwang, and J. M. Liu, Phys. Rev. Lett. 82, 1132 (1999). 10.1103/PhysRevLett.82.1132
14. M. A. Zaks, X. Sailer, L. Schimansky-Geier, and A. B. Neiman, Chaos 15, 026117 (2005). 10.1063/1.1886386
15. F. T. Arecchi, R. Badii, and A. Politi, Phys. Rev. A 32, 402 (1985). 10.1103/PhysRevA.32.402
16. A. Bulsara, W. C. Schieve, and E. W. Jacobs, Physica A 146, 126 (1987). 10.1016/0378-4371(87)90225-1
17. S. Kim, S. H. Park, and C. S. Ryu, Phys. Rev. E 58, 7994 (1998). 10.1103/PhysRevE.58.7994
18. U. Feudel and C. Grebogi, Phys. Rev. Lett. 91, 134102 (2003). 10.1103/PhysRevLett.91.134102
19. S. Kraut and U. Feudel, Phys. Rev. E 66, 015207 (R) (2002). 10.1103/PhysRevE.66.015207
20. S. L. T. de Souza, A. M. Batista, I. L. Caldas, R. L. Viana, and T. Kapitaniak, Chaos, Solitons Fractals 32, 758 (2007). 10.1016/j.chaos.2005.11.056
21. M. I. Dykman, R. Mannella, P. V. E. McClintock, and N. G. Stocks, Phys. Rev. Lett. 65, 48 (1990). 10.1103/PhysRevLett.65.48
22. M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, Phys. Rev. E 49, 1198 (1994). 10.1103/PhysRevE.49.1198
23. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems (Springer, New York, 1984).
24. M. Dembo and O. Zeitouni, Large Deviations Techniques and Applications (Jones and Bartlett, Boston, 1995).
25. I. A. Bashkirtseva and L. B. Ryashko, Physica A 278, 126 (2000). 10.1016/S0378-4371(99)00453-7
26. I. A. Bashkirtseva and L. B. Ryashko, Dyn. Syst. Appl. 11, 293 (2002).
27. I. A. Bashkirtseva and L. B. Ryashko, Math. Comput. Simul. 66, 55 (2004). 10.1016/j.matcom.2004.02.021
28. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963). 10.1175/1520-0469(1963) 020<0130:DNF>2.0.CO;2
29. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer Series in Applied Mathematics Vol. 41 (Springer, Berlin, 1982).
30. A. Zippelius and M. Lucke, J. Stat. Phys. 24, 345 (1981). 10.1007/BF01013305
31. J. Keizer, R. F. Fox, and J. Wagner, Phys. Lett. A 175, 17 (1993). 10.1016/0375-9601(93)90847-S
32. M. Dorfle and R. Graham, Phys. Rev. A 27, 1096 (1983). 10.1103/PhysRevA.27.1096
33. H. M. Ito, J. Stat. Phys. 35, 151 (1984). 10.1007/BF01017371
34. V. S. Anishchenko, D. G. Luchinsky, P. V. E. McClintock, I. A. Khovanov, and N. A. Khovanova, Sov. Phys. JETP 94, 821 (2002). 10.1134/1.1477907
35. J. B. Gao, W. Tung, and N. Rao, Phys. Rev. Lett. 89, 254101 (2002). 10.1103/PhysRevLett.89.254101
36. I. I. Fedchenia, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks, Phys. Rev. A 46, 1769 (1992). 10.1103/PhysRevA.46.1769
37. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
38. G. N. Milstein and M. V. Tretyakov, Stochastic Numerics for Mathematical Physics, Series: Scientific Computation (Springer-Verlag, Berlin, 2004).
39. M. Ryagin and L. Ryashko, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, 3981 (2004). 10.1142/S0218127404011600