Nonlinear Fokker-Planck equation exhibiting bifurcation phenomena and generalized thermostatistics

Journal of Mathematical Physics

Volumn 43, Issue 5, 2002, Pages 2654-2669

  Shiino, Masatoshi ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981820     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1467965     Document Type: Article

References (51)

1. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
2. E.M.F. Curado and C. Tsallis, J. Phys. A 24, L69 (1991).
3. C. Tsallis, R.S. Mendes, and A.R. Plastino, Physica A 261, 534 (1998).
4. A. Renyi, Probability Theory (North-Holland, Amsterdam, 1970).
5. Z. Daroczy, Inf. Control. 16, 36 (1970).
6. B.D. Sharma and D.P. Mittal, J. Math. Sci. 10, 28 (1975).
7. I. Csiszar, in Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and the European Meeting of Statisticians, 1974 (Reidel, Dordrecht, 1978), p. 73.
8. M.P. Schutzenberger, Contribution aux applications statistique de la theorie de l'information, Publ. Inst. Statist. Univ. Paris 3 (1954).
9. J. Harvda and F. Charvat, Kybernetica 3, 30 (1967).
10. I. Vajda, Kybernetica 4, 105 (1968).
11. C. Tsallis, in Nonextensive Statistical Mechanics and Thermodynamics, Series Lecture Notes in Physics, edited by S. Abe and Y. Okamoto (Springer, Heidelberg, 2000), and references therein.
12. A.R. Plastino and A. Plastino, Physica A 222, 347 (1995).
13. L. Borland, Phys. Rev. E 57, 6634 (1998).
14. G. Kaniadakis and G. Lapenta, Phys. Rev. E 62, 3246 (2000).
15. S. Martinez, A.R. Plastino, and A. Plastino, Physica A 259, 183 (1998).
16. C. Tsallis and D.J. Bukman, Phys. Rev. E 54, R2197 (1996).
17. T.D. Frank and A. Daffertshofer, Physics A 285, 351 (2000).
18. M. Shiino, J. Math. Phys. 42, 2540 (2001).
19. T.D. Frank and A. Daffertshofer, Physica A 295, 455 (2001).
20. T.D. Frank and A. Daffertshofer, Physica A 292, 392 (2001).
21. A. Compte and D. Jou, J. Phys A 29, 4321 (1996).
22. J.P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990).
23. G. Zimbardo and P. Veltri, Phys. Rev. E 51, 1412 (1995).
24. G.M. Zaslavsky, D. Stevens, and H. Weizner, Phys. Rev. E 48, 1683 (1993).
25. P. Rosenau, Phys. Rev. Lett. 74, 1056 (1995).
26. J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976).
27. F. Schlogl, Phys. Rep. 62, 267 (1980).
28. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
29. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
30. C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985).
31. M. Shiino, J. Phys. Soc. Jpn. 67, 3658 (1998).
32. S. Kullback, Ann. Math. Stat. 22, 79 (1951).
33. A.M. Mariz, Phys. Lett. A 165, 409 (1992).
34. J.D. Ramshaw, Phys. Lett. A 175, 169 (1993).
35. C. Tsallis, Phys. Rev. E 58, 1442 (1998).
36. L. Borland, A.R. Plastino, and C. Tsallis, J. Math. Phys. 39, 6490 (1998).
37. A.K. Rajagopal and S. Abe, Phys. Rev. Lett. 83, 1711 (1999).
38. M. Miyata, M. Yamada, and T. Kawaguchi, Rep. Math. Phys. 39, 19 (1997).
39. S. Amari, Differential Geometric Methods in Statistics, Lecture Notes in Statistics, Vol. 28 (Springer, Berlin, 1985).
40. M. Shiino, Phys. Lett. A 112, 302 (1985); Phys. Rev. A 36, 2393 (1987).
41. M. Shiino, Phys. Lett. A 112, 302 (1985); Phys. Rev. A 36, 2393 (1987).
42. R.C. Desai and R. Zwanzig, J. Stat. Phys. 19, 1 (1978).
43. D.A. Dawson, J. Stat. Phys. 31, 29 (1983).
44. A.N. Drozdov and M. Morillo, Phys. Rev. E 54, 3304 (1996).
45. M. Shiino, Phys. Lett A 111, 396 (1985).
46. A. Arenas and C.J. Perez Vicente, Europhys. Lett. 26, 79 (1994).
47. M. Yoshioka and M. Shiino, Phys. Rev. E 61, 4732 (2000).
48. H. Sakaguchi, Prog. Theor. Phys. 79, 39 (1988).
49. T.D. Frank, A. Daffertshofer, C.E. Peper, P.J. Beck, and H. Haken, Physica D 150, 219 (2001).
50. M. Shiino and K. Yoshida, Phys. Rev. E 63, 026210 (2001).
51. F.D. Nobre and C. Tsallis, Physics A 213, 337 (1995).