Chaotic and pseudochaotic attractors of perturbed fractional oscillator

Chaos

Volumn 16, Issue 1, 2006, Pages

  Zaslavsky, G M ^a,b   Stanislavsky, A A ^a,c   Edelman, M ^a  

^a NEW YORK UNIVERSITY   (United States)

^b POLYTECHNIC UNIVERSITY   (United States)

^c INSTITUTE OF RADIO ASTRONOMY   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645670923     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2126806     Document Type: Article

References (45)

1. O. Heaviside, Electromagnetic Theory, Vol. II (Chelsia, New York, 1922).
2. V. Bush, Operational Circuit Analysis (Wiley, New York, 1922).
3. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993).
4. G. M. Zaslavsky, Phys. Lett. 69, 145-147 (1978).
5. K. T. Alligood, T. D. Sauer, and J. A. Yorke, CHAOS: An Introduction to Dynamical Systems (Springer-Verlag, New York, 1996).
6. G. M. Zaslavsky, Physica D 0167-2789 10.1016/0167-2789(94)90254-2 76, 110-122 (1994); G. M. Zaslavsky, Chaos 4, 25-33 (1994).
7. G. M. Zaslavsky, Physica D 0167-2789 10.1016/0167-2789(94)90254-2 76, 110-122 (1994); G. M. Zaslavsky, Chaos 4, 25-33 (1994).
8. G. M. Zaslavsky, Phys. Rep. 371, 461 (2002).
9. A. Piryatinska, A. I. Saichev, and W. A. Woyczynski, Physica A 349, 375-420 (2005).
10. T. L. Szabo, J. Acoust. Soc. Am. 0001-4966 10.1121/1.410434 96, 491 (1994); D. T. Blackstock, J. Acoust. Soc. Am. 0001-4966 10.1121/1.391778 77, 2050 (1985); W. Chen and S. Holm, J. Acoust. Soc. Am. 115, 1424 (2004).
11. T. L. Szabo, J. Acoust. Soc. Am. 0001-4966 10.1121/1.410434 96, 491 (1994); D. T. Blackstock, J. Acoust. Soc. Am. 0001-4966 10.1121/1.391778 77, 2050 (1985); W. Chen and S. Holm, J. Acoust. Soc. Am. 115, 1424 (2004).
12. T. L. Szabo, J. Acoust. Soc. Am. 0001-4966 10.1121/1.410434 96, 491 (1994); D. T. Blackstock, J. Acoust. Soc. Am. 0001-4966 10.1121/1.391778 77, 2050 (1985); W. Chen and S. Holm, J. Acoust. Soc. Am. 115, 1424 (2004).
13. R. R. Nigmatullin, Phys. Status Solidi B 133, 425 (1986).
14. T. F. Nonnenmacher, in Lecture Notes in Physics (Springer, Berlin, 1991), Vol. 381, p. 309.
15. S. Kempfle, I. Schäfer, and H. Beyer, Nonlinear Dyn. 29, 99-127 (2002).
16. K. Weron and A. Klauser, Ferroelectrics 236, 59-69 (2000).
17. H. Weitzner and G. M. Zaslavsky, Commun. Nonlinear Sci. Numer. Simul. 8, 273-281 (2003).
18. N. Laskin, Phys. Rev. E 66, 056108 (2002).
19. E. Goldfain, Chaos, Solitons Fractals 0960-0779 10.1016/S0960-0779(03) 00304-7 19, 1023-1030 (2004); E. Goldfain, Chaos, Solitons Fractals 0960-0779 10.1016/j.chaos.2004.02.043 22, 513-520 (2004); E. Goldfain, Chaos, Solitons Fractals 23, 701-710 (2005).
20. E. Goldfain, Chaos, Solitons Fractals 0960-0779 10.1016/S0960-0779(03) 00304-7 19, 1023-1030 (2004); E. Goldfain, Chaos, Solitons Fractals 0960-0779 10.1016/j.chaos.2004.02.043 22, 513-520 (2004); E. Goldfain, Chaos, Solitons Fractals 23, 701-710 (2005).
21. E. Goldfain, Chaos, Solitons Fractals 0960-0779 10.1016/S0960-0779(03) 00304-7 19, 1023-1030 (2004); E. Goldfain, Chaos, Solitons Fractals 0960-0779 10.1016/j.chaos.2004.02.043 22, 513-520 (2004); E. Goldfain, Chaos, Solitons Fractals 23, 701-710 (2005).
22. I. M. Gelfand and G. E. Shilov, Generalized Functions I: Properties and Operations (Academic, New York, 1964).
23. S. G. Samko, A. A. Kilbas, and O. I. Marichev (Nauka i Technika, Minsk, 1987) (in Russian).
24. M. M. Meerschaert, D. A. Benson, H. P. Scheffler, and B. Baeumer, Phys. Rev. E 66, 060102 (2002).
25. I. Podlubny, Fractional Differential Equations (Academic, New York, 1999).
26. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993).
27. A. I. Saichev and G. M. Zaslavsky, Chaos 7, 753-764 (1997).
28. V. V. Uchaikin and V. M. Zolotarev, Chance and Stability: Stable Distributions and their Applications (VSP, Utrecht, The Netherlands, 1999).
29. A. A. Stanislavsky, Theor. Math. Phys. 138, 418-431 (2004).
30. F. Mainardi, Chaos, Solitons Fractals 7, 1461-1477 (1996).
31. R. Gorenflo and F. Mainardi, in Proceedings of the International Workshop on the Recent Advances in Applied Mathematics (RAAM '96)., Kuwait, 1996, Kuwait University, Department of Mathematics and Computer Science, pp. 193-208.
32. M. Seredyńska and A. Hanyga, J. Math. Phys. 41, 2135-2156 (2000).
33. A. A. Stanislavsky, Phys. Rev. E 70, 051103 (2004).
34. M. D. Ortigueria, Signal Process. 83, 2301 (2003).
35. Yu. Rabotnov, " Creep problems in structural members " (North-Holland, Amsterdam, 1969), p. 129. Originally published in Russian as Polzuchest' Elementov Konstruktsii (Nauka, Moscow, 1966).
36. M. Caputo, J. R. Astron. Soc. Can. 13, 529-539 (1967).
37. A. Erdályi, Higher Transcendental Functions (McGraw-Hill, New York, 1955), Vol. III, Sec. 18.
38. A. Chatterjee, Nonlinear Dyn. 0924-090X 10.1023/A:1025645620615 32, 323-343 (2003); P. Wahi and A. Chatterjee, Nonlinear Dyn. 38, 3-22 (2004).
39. A. Chatterjee, Nonlinear Dyn. 0924-090X 10.1023/A:1025645620615 32, 323-343 (2003); P. Wahi and A. Chatterjee, Nonlinear Dyn. 38, 3-22 (2004).
40. A. A. Stanislavsky, Physica A 354, 101-110 (2005).
41. K. Diethelm, N. J. Ford, A. D. Freed, and Yu. Luchko, Comput. Methods Appl. Mech. Eng. 194, 743-773 (2005).
42. L. D. Landau and E. M. Lifschitz, Mechanics, 3rd ed. (Pergamon, Oxford, England, 1976).
43. O. Lyubomudrov, M. Edelman, and G. M. Zaslavsky, Int. J. Mod. Phys. B 0217-9792 17, 4149 (2003); G. M. Zaslavsky and M. Edelman, Physica D 193, 128-147 (2004).
44. O. Lyubomudrov, M. Edelman, and G. M. Zaslavsky, Int. J. Mod. Phys. B 0217-9792 17, 4149 (2003); G. M. Zaslavsky and M. Edelman, Physica D 193, 128-147 (2004).
45. J. A. T. Machado, A. J. Calderón, and B. M. Vinagre, 5th EUROMECH Nonlinear Dynamics Conference, Eindhoven, 2005 (unpublished).