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A procedure for obtaining general nonlinear Fokker–Planck equations

Author

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  • Nobre, Fernando D.
  • Curado, Evaldo M.F.
  • Rowlands, G.

Abstract

A procedure for deriving general nonlinear Fokker–Planck equations (FPEs) directly from the master equation is presented. The nonlinear effects are introduced in the transition probabilities, which present a dependence on the probabilities for finding the system in a given state. It is shown that the FPEs, obtained from master equations describing transitions among discrete and continuous sets of states, are identical. Within such a procedure, we construct nonlinear FPEs that appear to be very general. Our general FPEs recover, as particular cases, nonlinear FPEs investigated previously by many authors, introduced on a purely phenomenological basis, and they lead to the possibility of more complete and complex diffusive equations.

Suggested Citation

  • Nobre, Fernando D. & Curado, Evaldo M.F. & Rowlands, G., 2004. "A procedure for obtaining general nonlinear Fokker–Planck equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 109-118.
  • Handle: RePEc:eee:phsmap:v:334:y:2004:i:1:p:109-118
    DOI: 10.1016/j.physa.2003.11.023
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    Cited by:

    1. Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Biró, T.S. & Néda, Z., 2018. "Unidirectional random growth with resetting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 335-361.

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