Mixing and spectral-correlation properties of chaotic and stochastic systems: Numerical and physical experiments

New Journal of Physics

Volumn 7, Issue , 2005, Pages

  Anishchenko, V S ^a   Okrokvertskhov, G A ^a   Vadivasova, T E ^a   Strelkova, G I ^a  

^a SARATOV STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOCORRELATION DECAY; CHAOTIC OSCILLATIONS; POWER SPECTRUM; SPIRAL CHAOS;

CHAOS THEORY; GAUSSIAN NOISE (ELECTRONIC); HARMONIC ANALYSIS; MATHEMATICAL MODELS; MIXING; SIGNAL PROCESSING; STATISTICAL METHODS; TRAJECTORIES;

RANDOM PROCESSES;

EID: 23244438756     PISSN: 13672630     EISSN: 13672630     Source Type: Journal    
DOI: 10.1088/1367-2630/7/1/076     Document Type: Article

References (50)

1. Broer H W, Dumortier F, van Strien S J and Takens F 1991 Structures in Dynamics. Finite Dimensional Deterministic Studies (Amsterdam: North-Holland)
2. Komogorov A N 1959 Dokl. Acad. Nauk. USSR 124 754-55 (in Russian)
3. Sinai Y 1959 Dokl. Acad. Nauk USSR 124 768-71 (in Russian)
4. Bowen R 1975 Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms (Lecture Notes in Mathematics vol 470) (Berlin: Springer)
5. Ruelle D 1989 Math. Phys. 125 239
6. Ruelle D 1976 Am. J. Math. 98 619
7. Ruelle D 1978 Bol. Soc. Bras. Math. 9 83
8. Bowen R and Ruelle D 1975 Invent. Math. 29 181
9. Eckmann J P and Ruelle D 1985 Rev. Mod. Phys. 57 617
10. Pesin Y 1977 Russian Math. Surveys 32 55
11. Christiansen F, Paladin G and Rugh H H 1990 Phys. Rev. Lett. 65 2087
12. Liverani C 1995 Ann. Math. 142 239
13. Froyland G 1997 Commun. Math. Phys. 189 237
14. Arneodo A, Collet P and Tresser C 1981 Commun. Math. Phys. 79 573
15. Lorenz E N 1963 J. Atmos. Sci. 20 130-41
16. Shilnikov L P 1997 Int. J. Bif. Chaos 1 1953
17. Afraimovich V S, Bikhov V V and Shilnikov L P 1977 Dokl. Acad. Nauk. USSR 234 336 (in Russian)
18. Ruelle D and Takens F 1971 Commun. Math. Phys. 20 167
19. Zaslavsky G M 1985 Chaos in Dynamical Systems (New York: Harwood Academic)
20. Renyi A 1957 Acta Math. Acad. Sci. Hungary 8 477
21. Rokhlin V A 1961 Izv. Acad. Nauk. USSR 25 499 (in Russian)
22. Afraimovich V S 1989 Nonlinear Waves - I (Berlin: Springer) pp 14-28
23. Anishchenko V S, Astakhov V V, Neiman A B, Vadivasova T E and Schimansky-Geier L 2002 Nonlinear Dynamics of Chaotic and Stochastic Systems (Berlin: Springer)
24. Afraimovich V S and Shilnikov L P 1983 Nonlinear Dynamics and Turbulence (Boston, MA: Pitman) pp 1-43
25. Anishchenko V S, Vadivasova T E, Kopeikin A S, Kurths J and Strelkova G I 2001 Phys. Rev. Lett. 87 054101
26. Anishchenko V S, Vadivasova T E, Kopeikin A S, Kurths J and Strelkova G I 2002 Phys. Rev. E 65 036206
27. Rössler O E 1976 Phys. Lett. A 57 397
28. Crutchfield J, Framer D, Packard N, Shaw R, Jones G and Donelly R J 1980 Phys. Lett. A 76 1-4
29. Farmer J D 1981 Phys. Rev. Lett 47 179-82
30. Pikovsky A, Rosenblum M and Kurths J 2001 Synchronization. A Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press)
31. Letellier G, Duterte P and Maheu B 1995 Chaos 5 271-82
32. Gilmore R and Lefranc M 2002 The Topology of Chaos: Alice in Stretch and Squeezeland (New York: Wiley)
33. Guckenheimer J and Holms P 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Berlin: Springer)
34. Jackson E A 1989 Perspectives of Nonlinear Dynamics vol 1 (Cambridge: Cambridge University Press)
35. Jackson E A 1991 Perspectives of Nonlinear Dynamics vol 2 (Cambridge: Cambridge University Press)
36. Rosenblum M, Pikovsky A and Kurths J 1996 Phys. Rev. Lett. 76 1804
37. Anishchenko V S 1995 Dynamical Chaos - Models and Experiments (Singapore: World Scientific)
38. Anishchenko V S, Vadivasova T E, Okrokvertskhov G A and Strelkova G I 2003 Physica A 325 199-212
39. Anishchenko V S, Vadivasova T E, Strelkova G I, Kopeikin A S and Kurths J 2003 Fluctuation and Noise Lett. 3 213
40. Anishchenko V S, Vadivasova T E, Okrokvertskhov G A and Strelkova G I 2004 Phys. Rev. E 69 036215
41. Gabor D 1946 J. Inst. Electr. Eng. 93 429
42. Rytov S M, Kravtsov Y A and Tatarskii V I 1987 Principles of Statistical Radiophysics (Berlin: Springer)
43. Osipov G V, Hu B, Zhou C, Ivanchenko M V and Kurths J 2003 Phys. Rev. Lett. 91 024101
44. Anishchenko V S, Vadivasova T E, Strelkova G I and Okrokvertskhov G A 2004 Math. Biosci. Eng. 1 161-84
45. Stratonovich R L 1963 Topics in the Theory of Random Noise vol 1 (New York: Gordon and Breach)
46. Stratonovich R L 1967 Topics in the Theory of Random Noise vol 2 (New York: Gordon and Breach)
47. Malakhov A N 1968 Fluctuations in Auto-Oscillating Systems (Moscow: Nauka)
48. Rytov S M 1966 Introduction in Statistical Radiophysics (Moscow: Nauka) (in Russian)
49. Tikhonov V I and Mironov M A 1977 Markovian Processes (Moscow: Sov. Radio) (in Russian)
50. Yamrom B, Kunin I and Chernykh G 2003 Int. J. Eng. Sci. 41 475-82