24
2 The Fokker-Planck Equation
15. Lo, C.F.: Exact propagator of the Fokker–Planck equation with logarithmic factors in diffusion
and drift terms. Phys. Lett. A 319, 110 (2003)
16. Sasaki, K.: Diffusion coefficients for two-state Brownian motors. J. Phys. Soc. Jpn. 72, 2497
(2003)
17. Zhao, C.Y., Tan, W.H., Guo, Q.Z.: The solution of the Fokker-Planck equation of nondegenerate parametric amplific ation system for generation of squeezed light. Acta Phys. Sin.
52, 2694 (2003)
18. Arnold, A., Unterreiter, A.: Entropy decay of discretized fokker-planck equations I–Temporal
semidiscretization. Comput. Math. Appl. 46, 1683 (2003)
19. Chhib, M., El Arroum, L., Mazroui, M., Boughaleb, Y., Ferrando, R.: Influence of the periodic
potential shape on the Fokker–Planck dynamics. Physica A 331, 365 (2004)
20. Kamitani, Y., Matsuba, I.: Self-similar characteristics of neural networks based on Fokker–
Planck equation. Chaos Solitons Fractals 20, 329 (2004)
21. Nobre, F.D., Curado, E.M.F., Rowlands, G.: A procedure for obtaining general nonlinear
Fokker–Planck equations. Physica A 334, 109 (2004)
22. Abe, S.: Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion. Phys.
Rev. E 69, 016102, Part 2 (2004)
23. Subramanian, G., Brady, J.F.: Multiple scales analysis of the Fokker–Planck equation for
simple shear flow. Physica A 334, 343 (2004)
24. Liang, G.Y., Cao, L., Wu, D.J.: Approximate Fokker–Planck equation of system driven by
multiplicative colored noises with colored cross-correlation. Physica A 335, 371 (2004)
25. Sparber, C., Carrillo, J.A., Dolbeault, J., Markowich, P.A.: On the long-time behavior of the
quantum Fokker-Planck equation. Monatchefte fur Mathematik 141, 237 (2004)
26. Oster, G., Hongyun, W., Grabe, M.: How Fo–ATPase generates rotary torque. Phil. Trans. R.
Soc. Lond. B 355, 523 (2000)
27. Risken, H.: The Fokker-Planck Equation: Methods of Solution and Applications. Springer,
Berlin (1984)
28. Crank, C., Nicolson, N.: A practical method for numerical evaluation of solutions of partial
differential equations of the heat-conduction type. Proc. Camb. Philos. Soc. 43(50), 50 (1947)
29. Press, W.H., Teukolsky, S.A., Vettering, W.T., Flannery, B.P.: Numerical Recipes, The Art of
Scientific Computing, p. 625. Cambridge University Press, New York (1987)
2 The Fokker-Planck Equation
15. Lo, C.F.: Exact propagator of the Fokker–Planck equation with logarithmic factors in diffusion
and drift terms. Phys. Lett. A 319, 110 (2003)
16. Sasaki, K.: Diffusion coefficients for two-state Brownian motors. J. Phys. Soc. Jpn. 72, 2497
(2003)
17. Zhao, C.Y., Tan, W.H., Guo, Q.Z.: The solution of the Fokker-Planck equation of nondegenerate parametric amplific ation system for generation of squeezed light. Acta Phys. Sin.
52, 2694 (2003)
18. Arnold, A., Unterreiter, A.: Entropy decay of discretized fokker-planck equations I–Temporal
semidiscretization. Comput. Math. Appl. 46, 1683 (2003)
19. Chhib, M., El Arroum, L., Mazroui, M., Boughaleb, Y., Ferrando, R.: Influence of the periodic
potential shape on the Fokker–Planck dynamics. Physica A 331, 365 (2004)
20. Kamitani, Y., Matsuba, I.: Self-similar characteristics of neural networks based on Fokker–
Planck equation. Chaos Solitons Fractals 20, 329 (2004)
21. Nobre, F.D., Curado, E.M.F., Rowlands, G.: A procedure for obtaining general nonlinear
Fokker–Planck equations. Physica A 334, 109 (2004)
22. Abe, S.: Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion. Phys.
Rev. E 69, 016102, Part 2 (2004)
23. Subramanian, G., Brady, J.F.: Multiple scales analysis of the Fokker–Planck equation for
simple shear flow. Physica A 334, 343 (2004)
24. Liang, G.Y., Cao, L., Wu, D.J.: Approximate Fokker–Planck equation of system driven by
multiplicative colored noises with colored cross-correlation. Physica A 335, 371 (2004)
25. Sparber, C., Carrillo, J.A., Dolbeault, J., Markowich, P.A.: On the long-time behavior of the
quantum Fokker-Planck equation. Monatchefte fur Mathematik 141, 237 (2004)
26. Oster, G., Hongyun, W., Grabe, M.: How Fo–ATPase generates rotary torque. Phil. Trans. R.
Soc. Lond. B 355, 523 (2000)
27. Risken, H.: The Fokker-Planck Equation: Methods of Solution and Applications. Springer,
Berlin (1984)
28. Crank, C., Nicolson, N.: A practical method for numerical evaluation of solutions of partial
differential equations of the heat-conduction type. Proc. Camb. Philos. Soc. 43(50), 50 (1947)
29. Press, W.H., Teukolsky, S.A., Vettering, W.T., Flannery, B.P.: Numerical Recipes, The Art of
Scientific Computing, p. 625. Cambridge University Press, New York (1987)